Tuning The Mandolin
First things first; a mandolin is tuned from the lowest/thickest strings to the highest/thinnest strings in the order G D A E. The strings are tuned in double courses, so really it's GG DD AA EE with there being two of each note.
The joke goes that a mandolin player spends half their time tuning the mandolin, and the other half playing out of tune. There is a little bit of truth in this, only in as much as mandolins generally do need to be tuned fairly often, and can go out of tune fairly quickly. The sooner you get used to keeping it in tune yourself the easier it'll be to do it quickly and painlessly.
Invest in a good tuner, for example the D'Addario Micro Tuner, or a Snark. These attach to the headstock and show you whether a note is sharp (too high) or flat (too low).
If a string sounds like it's flat or sharp (so lower or higher than it should be), then slacken off the string so it's flatter/lower than it should be, and tune up to the note you need. If you tune the note from above, or only by adjusting a little bit, then tension in the string (either in the nut, bridge or tailpiece) can sometimes mean it goes out of tune quickly as you pick a note and therefore pull the string.
You might notice the mandolin goes out of tune even when not being played. This is because changes in humidity and temperature can stretch and contract the wood of the instrument very slightly, pulling the strings now and again. So even if it was in tune yesterday, or two days ago (or a year ago!), it may not be the next time you play it!
As the strings are tuned in double courses, when you pick one string the same double string next to it can sometimes vibrate, which is also picked up by the tuner. Instead, when you pick a note, bring the pick to just rest on the next note to stop it vibrating.