Good searching takes place in three broad stages: planning, searching, and follow up.
In the planning stage, you line up tools to optimize organization and think about where you can and should search. You also begin to define your search question and translate it into a search strategy.
This merges into the search stage, where you will try out your search strategy in different databases and refine, refine, refine! You will collect records along the way, but you don't need to get the full text of these articles until you start the follow-up stage where you screen the records, first cursorily, then carefully.
Following this procedure for your searching helps ensure that you are actually catching the research most relevant to your question.
In the diagram below you can see the four steps you'll go through for a literature review.
*Adapted from: Moher D, Liberati A, Tetzlaff J, Altman DG, The PRISMA Group (2009). Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The PRISMA Statement. PLoS Med 6(7): e1000097. doi:10.1371/journal.pmed1000097. For more information, visit www.prisma-statement.org.