Please note that I am not a lawyer and do not consider the below to be legal advice (if anything, the below tries to make the point that you really should try to find a lawyer if and when you feel you’re not being treated fairly as a Candidate and your rights can only be upheld in a Court of Law).
Know Your Jurisdiction
Note that a lawsuit over a Federal Election (Presidential or Congressional) belongs in Federal Court. If you’re suing for Ballot Access, you’re typically suing the State’s Secretary of State and thus should file your suit in the court whose physical jurisdiction includes the State Capital (in other words, if you want to sue the State of Texas or one if the State’s election officials, your suit should be filed with the US District Court in Austin in Travis County).
The first step is to fill out the “Complaint for a Civil Case,” the form for which you should be able to find on the court’s website. The Complaint can be filed by Fedex if you’re filing from out of town or State.
Note that you’ll need to include a Cover Sheet.
The filing fee for a Federal lawsuit is $400 as of this writing (payable by money order (no checks)), and you do have the option to request a waiver of the fee, but note that consideration of such a request will hold everything up for a few weeks and the forms are extremely intrusive into your personal finances (you have to plead abject poverty and back up your claims with details).
Serving the Defendant
As the Plaintiff in the case, it’s up to you to serve papers on the Defendant, and that can get tricky. In these types of cases, service has to adhere to Rule 4 of the Federal Rules of Civil Procedure.
Also note that you have to separately request expedited consideration of your case and perhaps even request an injunction. Otherwise, if you’re trying to get on a ballot, that ballot could be printed and already on its way to voters who won’t be voting for you by the time you get your case heard if you allow that case to proceed at the usual glacial pace.
Lost yet? I myself dropped the case I filed. Get a lawyer.