A really tricky part of a case, and one that gets many pro se litigants confused, is the concept of the burden of proof.
Simply put, the burden of proof tells you who has to prove what, and what the standard of proving it is.
I know, it's a little confusing but let's try to simplify it.
First, if you sue someone else then the burden of proof is on you for most, if not all, of the case.
Let's take a car wreck case for example. If you sue someone because of a car wreck then you must prove 1) that the wreck was all or partially due to their intentional or negligent acts or omission and 2) that you suffered damages (personal injury or property) and 3) what those damages were. Since the burden of proof is on you, the defendant (the person that was sued) can sit back and do absolutely nothing and if you don't meet your burden of proof, then they automatically win.
In most civil cases the amount of proof you need is "by a preponderance of the evidence". This is a complicated way of saying "more likely than not". If you prove the case by 51%, then you win. If you only prove 49%, then you lose.
In criminal case the burden of proof on the prosecution is much higher. It is "beyond a reasonable doubt". While many criminal defense attorneys fail to take advantage of this heightened burden, a savvy one will impress upon the jury how onerous this is to the prosecution and of the few criminal cases that result in a not guilty, most cases are won because the attorney points out the holes in the prosecution's case.
There are some other burdens of proof, such as in punitive damages cases where the burden may be "clear and convincing" and occasionally a defendant has the burden of proof on an affirmative defense, but we'll discuss those on another post.
For now, the important thing to remember is that the burden of proof is on the Plaintiff and that burden is usually "by a preponderance of the evidence" (in non-legal terms, more likely than not).