If someone sues a person, corporation, etc. And they win the case or it says diposed, how can
A person find out what exactly the settlement was. Is this public information or private.
Where can I find it. I already know how to check the court case by name and index number,
But can't find the results when the case closed.

When a judgement is awarded the amount of the judgment is generally part of the public record, But if there is some settlement or what the exact amount that was actually collected is probably not part of the public record.

If someone sues a person, corporation, etc. And they win the case or it says diposed, how can
A person find out what exactly the settlement was. Is this public information or private.
Where can I find it. I already know how to check the court case by name and index number,
But can't find the results when the case closed.

If you have the style of the case (who vs. who) and the case number and know the courthouse where this case was filed you can go in person and have the clerk pull the actual Court file and you can sometimes find the final settlement in the file. This settlement would be there if the Judge had to approve of the settlement though. If no judge signed anything, then possibly you won't find the answer in the file. Just looking into the court's computer docket will not reveal the final settlement outcome. Docket entries are just abbreviated notes of the motion or the order entered.

Agree you will have to either go there yourself, or hire a paralegal to review the case in person and find out the facts

A court judgment would be in the court file, which is a public record. A settlement, however would possibly be agreed to out-of-court, in which case it would not be. In fact, many times, the settlement agreement specifies that the exact terms of the settlement will be confidential and the person who received the settlement is bound not to disclose what he received.