The drain line can become clogged, but can be cleaned with vinegar. A wet/dry vac can be used to remove bigger clogs.
Condensate Line, Condensate Drain
Cleaning a drain line is something that can be done by the homeowner. There is also the option to hire a professional, which can start at $75.
Costs vary greatly by region (and even by zip code). To get free estimates from local contractors, please indicate yours.