It depends how you define competent. I've been qualified for 8 years and I can still see areas I would like to improve on. I guess you mean how long is it before they're good enough for the paying public, and this would very much depend on a few things. I felt able to charge for my nails after I had qualified and practiced on my family and friends for about a year. I built up to it gradually, firstly working on my family and close friends for free, then extending it to my wider circle of friends, as they became reasonably decent I started to charge £10 to cover my materials and give me a bit besides to re-invest in materials and training. After a few months I was working on family, friends, friends of family and friends, and their friends, etc etc! Then I made the move to the salon, so it wasnt a clear cut move from practicing to doing it professionally, it was a gradual process of evolution as my skills grew.
You will always look at your nails and think "there's room for improvement", the moment you stop doing that you have big problems to be honest because there's always room for improvement!! So, dont wait until you hit perfection or you will never move on. There are certain basics you need to get a good grasp of eg smile lines, apex, c curve, product going very near the eponychium but not touching it etc, thorough prep etc. The important thing is to continue to invest in your training, and to keep practising regularly.