And so we come to the last clause of the contract:
27. English law
This Agreement shall be deemed to be a contract made in England and shall be construed and applied in all respects in accordance with English law and the parties hereto submit and agree to the jurisdiction of the English courts.
Obviously you only get this clause if you're in England. Or not so obviously.... I've had it in a contract with a publisher based in India and one in Scotland. If you and the publisher really are in England, you can't argue with this clause - you just are subject to English jurisdiction. And they have bigger sticks than you do.
OK, so now you understand everything, and you've argued about anything you don't like or didn't agree with. You might have argued about some extra things, just for practice - that's fine, I approve. If it has gone well, the editor/legal department will have removed clauses you don't like (such as waiving your moral rights) and will have reworded clauses as necessary (such as limiting the rights you are selling or licensing). If you have difficulty getting the publishers to change the contract, send the contract to the Society of Authors (if you are in the UK). If you're a member, their contract advice is free; if you're not a member, there is a small charge.
And if you're happy with it? Or at least willing to accept it? Take your favourite pen, sign it (initial every page if they want you to, have someone witness your signature if they specify that) and send it back.
Now you can open the champagne - congratulations!
Oh - and don't forget you have to write the book. I'm not here to tell you how to do that. Go and see that crabbit bat Nicola Morgan or someone.