Most new guitar players and even some experienced ones have trouble staying and playing in tune. I'll try listing here some of the common mistakes and there solutions.

When putting new strings on your guitar you must always make sure you stretch them as you tune them to pitch. I always hold them down on the neck around the 24th fret with my left hand while pulling them away from the guitar body with my right hand. You don't have to use too much muscle, a few firm tugs should do the trick.

Whenever you tune a string down in pitch, be sure to use the string stretching technique described above. Remember ALWAYS TUNE UP! It's always better when tuning down, to get close to the note, stretch the string and then tune up to the intended pitch.

You should purchase a quality tuner from a music store like zZounds.com . You don't need to spend your life's saving. An inexpensive tuner should be fine to start out. Remember, this thing will be traveling to gigs and jam sessions with you. I would recommend a good Boss tuner or Korg tuner. Both brands have low cost tuners that will do the job just fine.

If your guitar has a tremolo bridge, always remember that each string that you tune will go down in pitch as you tune the next string. One solution to this is to over tune the strings. That is to say, you may need to tune your low E string to an F in order to have it be around an E note by the time you finish tuning the other strings. Over time you'll get a feel for how much you need to over tune each string and it will become second nature.

If you play in a band, it is a good idea to always tune to the same pitch. Standard pitch is 440 but some bands like to tune down to 430 or even 420 for the heavier sound or vocal reasons or both. My point is that if you're practicing at 430 then you have a gig and your band tunes to 440, everything will suddenly sound different, your singer might not be able hit all the notes he or she did at practice, your solos might even sound wrong. This is because everything is now a half step higher in pitch. Make things easy on yourself, pick a pitch and stick with it, at practice and gigs.