Often large companies will have a standard document which they may expect you to adhere to. Read that carefully and make sure that you meet their criteria and that you are happy to go along with it.
In most cases, whether they do this or not, it is a good idea to draft a document stating exactly what the work is that you are undertaking.
Following an initial meeting send a letter or email thanking them and attach to this your contract. At the meeting you should have verbally agreed what you are going to do for the client and what they are going to give you in return. Unless it states in their terms of agreement to which you agree you should write in this by when you expect payment to be made. You should also state by when the work will be finished.
So, in essence, your letter of contract with the client should include a description of:
Your understanding of what they want and why
What you have agreed to deliver
The date by which the work will be finished
The process by which you propose to do the work (methodology)
The intended outcome
Your fee or rate of payment
The dates by which you want payment to be made
A statement of indemnity (if they ask and if you have it)
The document should be signed by you and a representative and the client
Make sure you include explicitly any unresolved issues that may remain ambiguous
And don’t forget to date the document.
Contracts can sometimes be more complicated than this. But these are just the basics and would normally be included in any contract or terms of engagement. It is also a good idea to send your client a draft document including all these points and asking them if they want to amend any of them.Contracts are often negotiated in the context so this is quite a normal thing to do.