Although the song was originally done with organ - it transfers to guitar very nicely. Even if you aren't familiar with this song, the melody is very strong and easy to pick up quickly. Here is the melody line (with some artistic variation) for this famous song on lead guitar. The song is in the key of C major, which means all the music, including the solo, is based around the C Major scale:
C Major Scale: C - D - E - F - G - A - B - C
Because the song doesn't use a guitar for lead voicing or phrases, we have a good opportunity to play to the strengths of your sacred axe. That means using bends, slides, vibrato, pull offs and some distortion / sustain to do things an organ just wishes it could do.
As you'll see here there are plenty of techniques and little lead phrases / licks employed to take the melody line and wander with it a bit. Because it's a classic tune with a particular vibe, we don't want to go all-out with full spandex warfare here. Just some mild distortion / gain and plenty of sustain (for holding long notes and getting the most out of vibrato). Using gentle, meaningful licks with a great melody line (like this song has) will work better with a song with this kind of feel than fast / heavy shredding. Don't get us wrong here, shredding is great stuff - but rarely works with moody 60's classics! Aim for a emotive style of playing (think Pink Floyd) and you get a different kind of power in your music.
Once you've got the melody, try it with the backing and experiment with your own improvisations / bag of tricks - e.g. trills, double bends etc. Don't forget, you can use the slower-paced ActionTab audio (rather than the normal speed audio) to help you get a slower, moodier feel for your lead! Stick to the C major scale and you can't go wrong.