Step One: The Torah talks about "should a man take a woman ..." (Deut. 24:1) which the rabbis interpret as kiddushin. The couple is therefore absolutely not married (at least via kiddushei kesef) unless he gives her a ring (or other item of value), before two kosher witnesses. Age-old practice is to do it under a chupah, though occasionally a couple may opt for a quick, simple chupa (usually a few people holding up a Tallis) and kiddushin at one point, then a big party some other time.
Step Two: Even though the couple would be married by kiddushin alone, the rabbis felt it wasn't right for a woman to live with the insecurity that if
her husband suddenly died or divorced her, she'd be penniless. They therefore decreed that a married couple must have a ketubah, a monetary document that says "the groom hereby agrees to provide for the bride after the dissolution of this marriage." It's executed by the signatures of two kosher witnesses, who need not be around for any other part of the ceremony. (In Ashkenazic practice, the ketubah is signed a few minutes before the chupah; in Sephardic practice, it's signed under the chupah.) The ketubah witnesses are simply vouching that he agreed to certain monetary responsibilities once the marriage is effective. A tricky question arises if the ketubah is signed before sunset (let's say Halachic Sunday, the 20th) and the kiddushin doesn't happen until nightfall (halachic Monday, the 21st) -- you have a document giving her certain rights as of the 20th, but they weren't married until the 21st.
Step Three: Tnaim. If two independent people meet up and decide to get married, that's great. But often in times past, there were complex negotiations between families about the terms of such (generally arranged) marriages. Thus, a binding document was executed (again, by two witnesses, who need not be present for anything else) at the time of the engagement between the two families, agreeing that this one's daughter will wed this one's son, with a penalty clause for cancelling the engagement without good reason. As time went by, people got increasingly nervous about signing such an agreement, until they weren't doing so until just before the wedding -- kind of a moot point to talk about binding agreements-to-wed. So Rabbi Moshe Feinstein rewrote the Tnaim based on the way it's commonly used today, i.e. five minutes before the wedding. The witnesses hereby certify "that all the involved families have satisfied all claims, holds, and demands, and that it is agreed that the couple may now wed and share their property without any further challenge." The Tnaim is done for tradition's sake -- especially if one used the agreement-to-wed language just before the wedding -- and the marriage is still completely binding without it.