Asalaamu Alaykum. My husband and I are new to Islam. We had an Islamic Nikah, but we did not realise that the marriage was a type of contract. We assumed it had the same principles of a non-Islamic marriage. But since learning that we can put conditions in our nikah contract the both of us would like to. Is too late to add conditions to the nikah contract? If we are able to add conditions how would we do this? Many thanks!
First of all what i'm saying is only my opinion and if somebody could give you any clear reference from Quran or Sunna you could consider it as nonsense.
Usually when you get married in Islam you have some Imam or someone considered as an earnest "scriber" this means someone you trust who writes down your conditions as a contract. Also you will need at least two witnesses. The Bride may need a Waly. And a Mahr (dowry) should be given to the bride or at least declared in the contract! And normally (this is a Sunna) the parents should announce (or at least the father of the bride) that you got married in your mosque/community/street/quarter.
Now you missed to do a contract and i can't see any reason why you couldn't catch this up. This means you will need an earnest scriber and at least two witnesses. I think (and this is really only my opinion) there is no harm if the scriber is a notary. You can read about contracts according to Islam in the surah al Baqara :
 O Believers, when you contract a debt for a fixed; term, you should put it in writing. Let a scribe write with equity the document for the parties. The scribe whom Allah has given the gift of literacy should not refuse to write. Let him write and let the one under obligation (the debtor) dictate, and he should fear Allah, his Lord, and should not diminish from or add anything to the terms which have been settled. But if the borrower be of low understanding or weak or unable to dictate (for any reason), then let the guardian of his interests dictate it with equity. And let two men from among you bear witness to all such documents. But if two men be not available, there should be one man and two women to bear witness so that if one of the women forgets (anything), the other may remind her. The witnesses should be from among such people whom you approve of as witnesses. When the witnesses are asked to testify, they should not refuse to do so. Do not neglect to reduce to writing your transaction for a specified term, whether it be big or small. Allah considers this more just for you, for it facilitates the establishment of evidence and lessens doubts and suspicions. Of course, there is no harm if you do not put in writing the common transactions you conclude daily on the spot, but in case of commercial transactions you should have witnesses. The scribe and the witnesses should not be harassed: if you do so, you shall be guilty of sin. You should guard against the wrath of Allah; He gives you the knowledge of the right way for Allah has the knowledge of everything.
 If you are on a journey and cannot find a scribe to write the document, then transact your business on the security of a pledge in hand. And, if any one transacts a piece of business with another merely on trust, then the one who is trusted should fulfill his trust and fear Allah, his Lord And never conceal evidence for he who conceals it, has a sinful heart: Allah knows everything that you do.
(Surah 2/Verses 282 and 283)
I would recommend you to do this as soon as possible and if you both agree about the contract everything should be fine! If not you should only put in the contract what you agree about (that again is only my suggestion). And maybe you should ask some Muslim friends for advices about the contents of the contract.
Welcome to Islam, you will soon witness the beauty of the religion, the peace and tranquility it brings to you and please don't be disappointed by the indiscipline among majority of its followers, we're trying, make supplication for us.
Congratulations on your marriage. May Allah put barakah in it and grant you pious children.
In Islam it is permissible for a man and woman to get married. And marriage is nothing but a word, a contract. Something that binds a man to be dutiful and obedient to his wife and fearful and obedient to commandments of Allah and the same goes for the wife.
Now only sane people can give a word and hold on to it. So we are talking about sane people. And since this question is about two muslims getting married, this answer isn't applicable for other scenarios.Sane people can also trick others and are also humans and can legitimately forget the vow they have taken so Islam requires that there be witnesses.
Now that this is such an auspicious event as it is helping stop corruption in the world (man and woman committing to each other and taking oath to stop adultery) , the Imam or the preacher recites a few verses from the Quran and takes an oath from you and you can get to private business.
Now things sometimes don't go as planned and comes in the issue of separation or divorce (which is very undesirable act in the eyes of Allah but Islam is practical and there is a space for exceptions).
A woman is under the protection of her wali (a male mahram care taker, simplest meaning) until her marriage, and when she gets married her husband becomes her wali. Now a woman could be in any condition when her divorce happens. So Islam stipulates that a woman seek appropriate Mahar (do not want to say dowry but meaning is close) at the time of Marriage, which she could spend with her own will. (Other intricacies involved here, lets not go there for now).
So going one step back, during the Nikah contract, you may or may not ask for Mahar and your husband may or may not pay it all upfront and may pay in installments. Anyhow all this goes in the contract and this is your right. (poor husband gets nothing right? Well he actually is getting a beautiful bride who will help him be a successful man)
All in all, Nikah is supposed to be simple with slightest of conditions yet a robust contract. There are possibilities of adding a million things, but in all fairness it is marriage not a business deal to put conditions and stipulations.
Also, unless IMHO if your conditions are like don't touch me until such and such date or you will let me commit haram or I don't want to have kids kind of conditions that could potentially disrupt the marriage then I do not see a reason to go back and change a marriage contract.
Allah knows best.