Forming a limited liability company makes it much harder to sue the LLC members. Like a corporation, an LLC is a separate legal entity from the owners. Someone can sue the LLC and clean out its business assets, but the member's individual assets are off-limits. Even if the LLC has no money, the owners usually are safe. Under the right circumstances, though, a plaintiff or creditor can collect from the owners too.
The LLC Name
You can sue an LLC for the same reasons you'd sue any business, such as fraud, negligence or unpaid debts. Learn your state's rules for such suits, and follow them to the letter. The Maryland People's Law Library says, for example, that you must use the LLC's exact legal name, as filed with the state. The California Courts website says if the LLC has a "doing business as" legal name, you should include that. If you have grounds for suing LLC members, name them as well.
Filing the Suit
Every LLC has to appoint a registered agent, who receives legal papers paperwork. You can find the name of the registered agent and the official name of the LLC in the paperwork filed with the state. However, your state may not require the company to list its members. Delaware, for example, doesn't include that information in state records. This makes it difficult to identify who you should sue, unless you've already had dealings with the members.
Piercing the Veil
Despite the liability protection LLCs offer, there are grounds for filing suit against members. If a member personally guarantees a loan, she's on the hook if the LLC doesn't pay. A member also is vulnerable if she personally injures you -- cheating you, for instance, or carrying out her role at the LLC with gross negligence. If there are multiple members, the loss of liability protection is an individual case -- one member's vulnerability doesn't affect the others.
Another argument for suing the owners is if you can show the LLC and its members aren't really separate entities. For example, if the company doesn't have its own bank account and all the funds are in the members' personal accounts, that's evidence a court should treat them as one person. This is a common problem with one-person LLCs. However, it'll be up to the judge in the case to make the call.