It can be as easy as you want to make it - or as hard as you want if you now hate each other! I went through the same thing 4 years ago.
First, get a valuation. Your local estate agent will do this free of charge.
Find out exactly what is left to pay on your mortgage (if you have one).
Work out how much would be left if you sold the house and paid off the mortgage.
Work out a fair percentage of this money - i.e. if you both paid half the deposit and half the mortgage, it would probably be 50%. Take everything into consideration - for example, if one of you has paid all the mortgage, but the other has paid all the bills, be fair!
Try and come to an agreement - whether you sell the property, or whether one will buy out the other.
You will need to see a lawyer, and you won't be able to both use the same one. It doesn't have to be expensive though, especially if you can both say 'this is what we've agreed to and we are both happy, all we want you to do is finalise it'.