Minimum requirements for marriage:

Set up by God

The Bible says in Genesis 2:18 "Then the LORD God said, 'it is not good that the man should be alone; I will make him a helper fit for him.'"
Genesis 1:27 & 28 says "So God created man in his own image, in the image of God he created him; male and female he created them.
And God blessed them. And God said unto them 'Be fruitful and multiply and fill the earth and subdue it, and have dominion over the fish of the sea and over the birds of the heavens, and over every living thing that moves on the earth.'"
Genesis 2:24 says "Therefore a man shall leave his father and mother and hold fast to his wife, and they shall become one flesh."
(This is also repeated in Matt 19:5 & 6)

Minimum requirements

The original requirements for marriage was to LEAVE your parents, CLEAVE to your husband/wife, and to have children by being "one flesh".
The leaving part requires the forming of a new family unit separate from the two sets of parents.
The cleaving part requires the commitment of the two people to stay together
The "one flesh" part requires sexual intercourse.

If two people on a dessert island decide to live together in a committed relationship before God, that counts as marriage.
That's the original bare minimum. No legal or religious authority needs to be involved.

Modern day legal USA marriage:

Legal criteria

Romans 13:1 tells us we need to be subject to the governing authorities. For US residents these days that means a couple who wants to be married needs to file a marriage license and have 2 witnesses sign it. There is a fee to pay too. From a legal standpoint that couple is married. (Afterwards the marriage certificate is issued.)
People were getting married before formal governments existed, so that is beyond he minimum. Many governments today have no requirements on marriage ceremonies, but the U.S. has this legal requirement to formally move someone from single to married.
Common law marriage (where you are considered married after a certain number of years living together but wihtout a marriage license) is only legal in 11 states, and dropping. Alabama used to be one of those states but outloawed it.

Respecful and wise marriage:

Social

From a social standpoint, getting married is a big change. It is important to communicate to your peer group and your community in general that neiher of you is available any longer. A ring on the 4th finger of the left hand is a nice reminder, but rings are not a requirement of marriage. A good way to communicate this significant change in status is to hold a semi-public ceremony and invite anyone who is significant in your life. Another way is to send out announcements. Whatever way it is done, it is important to make a clear announcement that this change has taken place.

Family

Adding a new member to the family is a big deal and should be recognized as such. How this is done may vary. The current family members need to meet the new person and start a relationship with them in order to keep the family ties strong. A gathering of the family at the time of the wedding is an opportune time to do this. The Bible has a general principle to honor your parents (Exodus 20:12). How the couple honors thier parents may come in many forms and may depend on the parents and the culture. Typical ways of honoring is to ask for the parents blessing, include them in plans for the wedding, invite them to any ceremonies, celebrations, and meals - and other things.

Religious community

The church/synogogue/mosque is an important part of your community, so the leader of your spiritual community should also be involved. Generally he(she) leads the ceremony.
The Bible has many examples of marriages wihout a pastor or priest being present but, similar to the family section, it is wise to include the important people and groups in your life as part of this important decision.

Biblical Christian marriage:

Spiritual commitment

Most weddings include a time where the couple vows to be faithful to one another "for better or worse, richer or poorer, in sickness and health, to love and cherish until death do us part". It is also an opportunity to publically commit to following the biblical standard of marriage. There is generally an "I do" statement from each person.
You can be legally married but not be committed to following God's standard for marriage. In order to be God honoring we need to make that commitment to God, as well as to our spouse.

Specifically Christian

It is not a "Christian marriage" unless there is a Christian pastor/priest officiating.

Biblical responsibilities

  1. Show love toward one another
  2. Wives submit to your husbands (Eph 5:22)
  3. Husbands love your wives as you do your own body, as Christ gave himself for the church (Eph 5:25)
  4. Husbands give honor to the wife (1 Peter 3:7)
  5. Wives reverence her husband (Eph 5:33)
  6. Do not abstain from sex for too long unless you are both in agreement (1 Cor 7:5)
  7. Partner together in raising the children

Related subjects

Arrangement

The Bible has many examples showing marriages being arranged but does not appear to command it. Many societies have demonstrated for centuries that a considered arrangement can work out just as well as couples forming on their own. My opinion is that parents have experience at marriage and know what attributes of a person are likely to work well for their child, who they know fairly well. A parent's opinion or blessing on the marriage is wise for the young adult as well as fulfills the Biblical command to honor your parents (Exodus 20:12).

Sex

Can you have sex and not be married? Yes, the Bible calls this Fornication (and is sin).
Can you be married and not have sex? Yes, in the same sense that you can be a Christian and not have done any good works.
This happens in unusual situations where it is not possible to carry out the natural intent and implications of the vow given (like he theif on the cross).

Financial cost

It is poor stewardship to spend too much on a wedding compared to other essentials of life. Only spend what you can afford.
Having a large expensive wedding can be a signal of wealth in a family so many people desire to have a large grand wedding, even though they cannot afford it. On the other hand, if a family can afford to hold a larger celebration of this important life event, there is certainly nothing wrong with spending some money.
It is worth noting that Jesus attended at least one wedding where there was extended celebration and wine.

Timing

The Bible says it is better to get married than to "burn" (1 Cor 7:9)
The implication is that sexual desire is a burning flame that can only be put out by consummation.
I believe it is wrong to be committed to one another and delay the wedding due to planning issues. You can certainly delay a ceremony but you should not delay the actual wedding if the commitment is solid. Delaying the marriage may cause unnecessary temptation to sin.
Yes, sex before marriage - even for an engaged couple - is sin.
So, waiting too long is wrong. Is there such a thing as going too fast? Yes.
The book "call it love or call it quits" argues persuasively that it is wise to experience how each of the seasons affect the person you are considering marrying. This allows you to see how they treat each of the yearly holidays, birthdays, natural events, social events, etc.
I recommend the time between the first meeting and the wedding be at least a year, but there is no Biblical command around this. That's just my opinion.
Similarly, I recommend both people be old enough that they know the general trajectory of their lives. When people are young they make a lot of the largest decisions of their lives. Marriage should be entered AFTER the other large decisions are made. It is a difficult situation to have your spouse choose their profession and their interest in having children AFTER they are marrried. I have seen many sad scenarios where that order was reversed to unfortunate affect.

Ending a marriage

Romans 7:2 says marriage only lasts until one of the couple dies. The remaning person is free to remarry afer that.
1 Cor 7:15 says that if you are married to an unbeliever and tha person leaves, let them leave.
Deut 24:1-4 says if the wife displeases her husband and he hands her a certificate of divorce, she is free to go marry someone else. (I assume it also works in reverse, though I do not know of any proof).
Deut 24:1-4 also says if the husband divorces his wife, the wife remarrys, and the second mariage ends, the first husband cannot take her back. God considers this an abomination.
Matthew 19:9 says if you get divorced for a reason OTHER than sexual immorality and get remarried you are committing adultery (the sin of having sex with antoher person while you are still married).
Mark 10:9 and Matthew 19:4-6 quote Jesus saying "what God has joined together, let no man separate", so Jesus is displeased with divorce.
Mark 10:11 & 12 says if a man divorces his wife and remarrys, he commits adultery, and vice versa. (This is in agreement with Matthew 19:9, it just leaves out the exception).

Summary: The marriage ends when one person dies, when an unbelieving spouse leaves, or when there is a divorce.
Getting remarried is only permitted if one partner was sexually unfaihful (in real life, not in your head)

A note on abuse: Being married is not the same as living together. If there are safety reasons the two married people should separate, that may be a wise decision for a time. This is not divorce but protection.
The couple shuld work on reconciliation while separate.

Best next steps

If you are single, it is a good thing to seek marriage. Get Godly counsel from more than one person before tying the knot.
If you are married, seek reconciliation and forgiveness with one another and stay together.
If you have already separated, seek to get back together with your spouse.
If have have already divorced and your ex-partner has not been sexually unfaithful, do not remarry.
If you have already remarried and your ex-spouse was not unfaithful, get Godly council. I'm not sure what to say.