If you are considering a legal malpractice suit, the first thing to think about will probably be, "Which type of malpractice applies here?" There are several types of legal malpractice: breach of contract, breach of fiduciary duty and negligence. The first two may be simpler to prove - it's easy to see where a contract has not been fulfilled, or see a history of money spent to examine whether fiduciary duty has been upheld. Negligence, on the other hand, has a standard set of four points that you, as the plaintiff or injured party, must prove in order to be successful in your suit.
The first thing to prove is that the accused lawyer (the defendant) did, indeed, owe a legal duty to the plaintiff. It doesn't require a signed contract or money to change hands, either: if a lawyer gives or promises to give you legal advice, they owe you certain things, including confidentiality, a certain standard of care and a certain level of communication. If your lawyer fails to provide any of these duties, you may have the beginnings of a case for negligence.
You must prove that your lawyer did, in fact, breach at least one of their duties. The standard here is that the defendant would have breached their duties if they failed to do something that a "reasonably prudent person" would have done in that situation. Another component of proving a breach of duty is that the defendant must have known that not performing the particular duty would cause harm. There is a standard "Rules of Professional Conduct" that all lawyers must follow - if a lawyer does not follow this standard of conduct, they may be liable for negligence.
Proving causation can be trickier. In this step, the plaintiff must prove that without the damaging actions of the defendant, they would not have been harmed. In some cases, this may mean that the plaintiff must prove that they would have won their previous lawsuit without the harmful effects of the defendant's actions.
The final piece of proving negligence is that the plaintiff must be able to place a monetary value on their experience. This can be the money that the plaintiff would have won in their prior lawsuit, medical expenses, monetary damages or any other sort of expense incurred due to the defendant's actions.