Essentially the same as anything - you need to prove that you have a cause of action (ex: breach of contract) sufficient to grant the relief you seek (monetary award, return of property, etc.). You'd also need to know the person or company's real name as it would be pretty hard to get that information from just a bitcoin address (also you'd need a person/company to make the order against as there's no bank or central authority that a court can compel to return the bitcoins). If it's a contract you don't necessarily need to ask the court to unwind the contract (give you back what you put in) but you could ask, for example, for the court to force the person to complete the contract (ex: give you the money you traded the bitcoins for instead of your bitcoins back)
Courts have a history of midunderstanding/screwing up technology-related decisions. Expect to have to explain bitcoin in detail and expect to be frustrated that the judge won't understand what it is (although you could get lucky). For this reason, depending on the fact scenario, you might have more success suing for monetary damages instead of the return of property (crypto currencies are still very much a grey area).
In most jurisdictions I believe the successful party is entitled to costs as well (basically if you had to sue someone and you were right they should pay your court costs). However in practice costs are almost never awarded in full (you'd get awarded a fraction of your legal costs) and even then getting the money out of the person can be difficult.
Which brings up another point - getting a judgment against someone is only the FIRST step in your battle. Assuming there are no appeals you can then try to enforce against the person but just because you show up at someone's door with a court order for them to do something (ex: pay you money) doesn't mean they will. It is common for parties to obtain judgments which they will never collect on .
It's probably not the amount of money but the source that matters. I don't think most lawyers would work on contingency even if the claim was for $10,000,000 if the defendant is a person without significant resources (as I said above, getting a million dollar judgment doesn't mean anything if you can't collect - can't get blood from a stone). You're probably thinking of personal injury lawsuits which, while they can easily run from the tens of thousands to the millions the defendants are usually insurance companies who are far less likely to frustrate a judgment - not including appeals ha ha. Basically if the lawyer puts thousands of dollars of work into a file he wants to be able to take his slice of the pie at the end.