Step 1: The plaintiff (person suing) files a complaint against a defendant (person being sued) to recover damages or receive compensation (usually money)...this can be for a variety of things.
Step 2: Going to Court--a judge and sometimes a jury may decide the case. Remember, a Civil case includes one person suing another person (not the government taking you to court--that's a criminal case!)
Step 3: The case can be appealed by either side to the Court of Appeals and the Virginia Supreme Court. Remember an appeal is heard if either side feels there was unfair treatment. Appeals are often heard in the Court of Appeals and the Virginia Supreme Court.
A note on Contracts
A note about contracts: When you sign a contract--a roommate you're paying rent to, for instance, you agree to do whatever the written piece of paper says. This is written down--if both parties agree to something they MUST uphold this. If one party does not it can be taken to Civil Court.