There's also something to be said for learning one particular database well, before branching out to others. The skills acquired in become familiar with one will be transferable elsewhere. One of the most important skills to learn is boolean searching. This means including and excluding terms within the same search. Beyond trial and error.
Many libraries offer mini-courses.
Or, you can sit down and do a search with someone more skilled than you. It's a quick way to learn some of the basic approaches and short cuts. Get a copy of any documentation. If there's a database that you anticipate using, get a copy of any documentation available. Some databases provide the option of actually downloading these background documents.