Save your downloads to a folder in Google Drive or Dropbox. This allows you to pull up your tabs on your phone during a jam session.
Free tabs are usually created by fans, not the original artists. This means they aren't always 100% accurate. Use the tab as a roadmap, but always listen to the original recording to get the rhythm and "feel" just right.
Look for "Text" versions or "Guitar Pro" files. If you have the right software (like TuxGuitar), you can download these files for free and play them back. 2. Songsterr