I've been taking lessons from several different teachers for my other instrument and talking and listening to many other musicians for the last three years, and this is what they say, take it measure by measure, very slowly at first and making sure that you play each measure technically correct (at least most of the time, perfection takes a little longer so be reasonable...) and in time. Use a metronome, because music without correct timing is just noise. You will also be surprised how much easier it is to play well with a metronome. Tap your foot with the metronome, so that over time you will have the rhythm 'absorbed' into yourself and you can play the song rhythmically every time without the metronome, like a real pro :)
When you have nailed one measure, add another, and as you learn each measure, go back to review all preceding measures, then learn the next measure.
Before you know it, you have memorised the whole lot.
Remember to review the newly learned tune every day for the first week and then every other day, finally you will need to review it once every week. At this regular repetition stage, you should start to improve on your technique. Record yourself and let someone competent review it and provide you with feedback.
Don't make age an excuse for anything :D
The accidental guitarist.