When tuning your drum skins you need to make sure to tighten the tuning pegs evenly (1/4 of a turn each time). In addition, make sure to tune the pegs in the correct order (see picture below) so that the tightening pressure on the drum head is distributed evenly. The key word to remember here is 'Star Shape'. This is the word that they look for in drum exams, (rockschool) when asked in the general musicianship questions.
You should ideally tune your drums regularly to keep them sounding nice.
Q: How do you tune a snare drum?
A: In a star shape, tighten or loosen the lugs with 1/4 turns or less until you reach the sound you are looking for.
Q: How do you replace a snare drum head?
A: Loosen all the lugs and take them out before taking off the snare rim and the old head. Clean out the snare if needed, then put the new snare head onto the drum, and then feed through the metal lugs and finger tighten them. Press down in the centre of the head to settle it into place. Next go round the lugs in a star shape tightening with quarter turns. After a few times around the star shape press the head again to stretch it a bit. Tap next to the lugs and make small adjustments if some sound tighter than others. Then keep going around in the star shape with quarter turns until it's sounding how you like it. Finally push down hard in the centre for a couple of seconds, and then fine tune the lugs with tiny turns if you think they need it. Tap next to the lugs to check if any are too tight or loose.
When you set up your drums for a show, make sure to fine tune the drums if there are any wobbling tones on your drums.
When recording in a studio, make sure you spend extra care to get the right tuning for the music you are recording before you actually go there. Again, you can fine tune when you are set up in the studio, but you don't want to be spending studio time doing this for too long if you are on a budget as it's probably going to be costing a lot of money. If your band mates see you wasting time tuning, they'll probably get annoyed if they are splitting the cost with you.
Some players fine tune for each song, or tune to specific musical notes on the toms when recording.