That's how a lawsuit is started. But there are pleading, procedural and evidentiary issues that could come up. You mentioned that you've been slandered for 31 years. The problem is that defamation actions (slander is spoken defamation) have a 1 year statute of limitations in Colorado. That means that you can sue for defamatory statements made about you in the past year, but for any of the other 30 years preceding that, the statute of limitations would preclude winning your lawsuit. Furthermore, you need to prove the content of the statements, that they were statements of material fact, that they were false, and that you suffered quantifiable economic damages (a specific dollar amount) due to these defamatory statements made within the past year.
Now assuming that you can prove that, then yes, you could sue in court for those damages. The burden of proof is on you to prove those damages, as well as all the other elements of defamation (the statement, that it was a statement of material fact and not opinion, that it was false, that it was communicated to a third party, and that it resulted in economic harm that you can quantify to a specific dollar figure. If you can prove that and overcome any objections of the other side, then you can win. But you win a judgment, which is a piece of paper. It means that you can attempt to collect that from the other side, but if they don't have any assets, then the piece of paper is worth just that: a piece of paper. So that's also something to consider, whether or not you can recover anything from the other side.
So to SUE someone, it's pretty simple. But to win your lawsuit is more complicated, and I would suggest that you at least contact an attorney in your area that deals with breach of contract cases. Go to www.lawyers.com or www.legalmatch.com to find an attorney in your area. You should be able to find one that will give you a free initial consultation and better advise you of your rights, any problems with your case, likelihood of success, how courts are treating cases such as yours in your area, and what you should do next.
Even if you go "pro se" (without an attorney), at least go to the library and check out a book or two on representing yourself pro se. There's a learning curve, but a little knowledge can prevent a potentially catastrophic failure. If you do it wrong, you might get dismissed on a technicality, and not even get to the substantive portion of your case.