How do I go about filing a lawsuit on a friend who I lent money to but who has failed to pay me back by the contract deadline?

For several hundred dollars through, say, $2,000 or $3,000, you're better off filing a small claims case and representing yourself pro se (acting as your own attorney), to save on legal fees. You would file a summons and complaint with your court, which would then serve them on the defendant; in the complaint, you lay out the facts and the basis for the suit, such as that you loaned the friend $X on such-and-such a date, if there was or was not a promissory note or other agreement, the terms of the loan and when it should have been repaid, and the fact that it was not repaid. You can get instructions and sample forms through the small claims court.

For more than $3k, you're probably best off hiring an attorney to sue on your behalf. Good luck.

You can sue your friend for breach of contract.  Depending on the amount of the loan, you may be able to file your lawsuit in Small Claims Court.  Your damages (the amount of compensation you are seeking in your lawsuit) should include the amount of the loan plus interest plus court costs.  Court costs would include the court filing fee and process server fee.

You can obtain the forms you will need to file your lawsuit for breach of contract from the court.