Construction attorney here. I handle contractor abandonment cases regularly and wanted to provide some specific legal guidance since the thread has a lot of general advice but is missing some important details.
When a contractor leaves a job incomplete, your remedies depend heavily on whether you have a written contract and what state you are in. In most jurisdictions, you can pursue a breach of contract claim for the cost to complete the work using another contractor, minus any unpaid balance. This is the standard cost of completion damages measure under Restatement (Second) of Contracts Section 348.
However, before you spend money on litigation, check whether the contractor is licensed. In states like California (Business and Professions Code Section 7031), an unlicensed contractor cannot enforce a contract or collect payment, and you may be entitled to disgorgement of all amounts paid regardless of work completed.
Practically speaking, for amounts under $10,000, small claims court is usually your best option. Filing fees are typically under $100, and you can get a hearing within 60-90 days. Bring your contract, photos of incomplete work, and a written estimate from another contractor showing the cost to complete.