This department deals with litigation and all other aspects of law which may or may not be litigious in nature such as wills/estate planning, incorporating businesses, contract drafting, real-estate transactions, disputes with administrative bodies, and more. Typically however, litigation will transpire when things go wrong and the controversy ends up in a court setting.
Lawsuits are initiated by filing what is called a Complaint. There are many other procedural requirements you need to follow to obtain jurisdiction over the other party. You need to have reason to sue and typically you will have to prove your elements to a judge or jury. Depending on where you sue and the amount in controversy you may or may not be able to get discovery (i.e., get evidence including interviews and documents of other people including the other party).