My friend and I bought a house together butshe no longer wishes to pay for her share, how do I go about filing to force her out?

Partition is the correct remedy that you'd sue for.  Since the property can't be physically divided, the court will order that it be sold, and the court will decide how any net proceeds or deficiency get split up.  You might have to pay the mortgage to prevent foreclosure, and if you do that, you should ask the court to take the payments she should have made out of her share of the proceeds, to reimburse you.  The detail issues in these cases, about who owes how much, for what, to whom, can get fairly involved, and your best bet is to have an attorney's help with this.