Low to high, a mandolin is G D A E: G3, D4, A4, E5. Every note is a pair of strings, so eight strings, four notes. Tuning it is really two jobs. Get each pair to the right note, then get the two strings in each pair to agree with each other.
Mandolin is tuned in fifths, which makes the by-ear method nice and regular. Get the G pair close to G from a reference, then:
Tune one string of the pair first, then play both together and bring the second one up to it. When they're close but not quite matched, you'll hear a slow wobble. That's beating, and it gets slower the closer you get. When it stops, you're there. It's the most satisfying part of owning a mandolin, and also the most annoying.
Same rule as any stringed instrument: tune up to the note, never down to it, and check everything once more at the end because the bridge on a mandolin floats and will happily drift while you work.
The Chartless tuner has mandolin targets, and once you're in tune it'll chart the chords of whatever song is playing, drawn as mandolin shapes.
More: free online tuner · mandolin chord chart · how to tune a banjo · all guides.