This one is easy.... it takes as long as you like. You will never truly master the guitar and each and every style but rather you will specialise in an area. The majority of guitarists fall into the 'oh I know a few chords' category. So they can play a handful of songs quite well and sometimes sing too. Most often 'Wonder Wall' is played or the low E string version of 'Smoke on the Water'.
These guitarists are very popular and are always great at parties.
Then there is the guitarist that plays a little more in depth with a particular style, say blues or country and enjoys learning songs of that genre but is a little more knowledgeable with scale theory and has mastered some solos on the guitar and is probably in a band.
Then there is the advanced guitarist who has many years experience in many styles and has loads of knowledge in musical theory, sometimes classically trained, and either performs or teaches or both. Each level takes a different amount of time but I think the advanced guitarist NEVER stops learning. The guitar becomes somewhat part of their life and is forever enjoyable and therefore does not seem like a task to learn new songs regularly. Thanks to YouTube we can see great guitarist reinventing the guitar and it's use on a regular basis.
By all means don't let this discourage you, nobody says what level you have to be at to call yourself a guitarist. Just play and enjoy the music! Not all of us are going to be the next Jimmy Hendrix so just admire him and keep learning at your own pace, I promise you will get there. Be a little bit better than you were yesterday and you will be a guitarist. Small steps will get you there.
If you want to try some free guitar lessons check the ones out on my website!