I am a clarinetist/saxophonist also getting into jazz, but most of the same things will apply.

Much of jazz is based on “standards” or common tunes that people play. You can pick up a “real book”, which is like the jazz standard bible, or you can find a PDF online of an older version. Certain Places will have their own set of standards which they like to call and know well. Many jazz musicians know these tunes, the melody and the chords and all. If they don’t know a tune, they can learn it by ear or check something like a real book. This includes the chord progression, key, melody, etc.

That’s how they learn tunes, but that’s not how they play them. Jazz, like any form of music, has stock skills. Scales, chords, arpeggios, licks, that sort of stuff. A lot of jazz musicians practice these on multiple keys, so that no mater what they are playing, they have the skills to play. So, most of the groove type of stuff is often just taking those stock skills and applying them to whatever chord progression the group is playing (it’s not always what is on the lead sheet, so watch out). It seems magical, but after enough practice, these things become automatic.

So, just like anything, practice you scales and chords, learn your theory, TRAIN YOUR EARS, and most importantly, play. Play a lot. You will pick up a lot of things like groove and improvisation as you play more and more. Your time in the practice room just gives you mechanically keep up and perform. The experience of playing teaches you how to play music.

I’m a semi-pro jazz piano player (meaning, I’m good enough to get paying gigs, but I don’t do it for a living). I’ve definitely performed solo piano many times. I know it’s not quite the same as guitar but hopefully it’s still insightful.

You use the term “sight reading”, but I would never perform a piece I’d never seen or heard before solo. If I’m playing solo, I get to pick what I play, so why would I play something I hadn’t rehearsed?

Now, that doesn’t mean that I might not pull out a piece I’d never performed solo before. There are lots of jazz standards that I’ve played many times in a trio or quartet, so I’ve heard and played the song many times before, but I never had to play the melody, chords, and bass line solo. I’m a strong enough player that I’d be comfortable coming up with a solo arrangement on the spot - but it’d depend on the piece, of course.

I’d definitely use a lead sheet for that, but I’m not sure I’d call it “sight reading”, because I know the song. The lead sheet is there to remind me of the exact notes, rhythm, and chords, so that I’m not relying 100% on memory. It takes all of the pressure out of trying to remember exactly what chord to use - but to be honest, if it’s a piece I’m going to play solo, I’ve probably played it enough times that I could get it 95% correct just from memory and by ear.

When playing in a group, that’s completely different. I’ll sight read new pieces all the time. If someone else knows the melody and all I need to do is play the chords, that’s super easy. By the time they’ve finished the melody and played the first solo, I’ve got the feel for the piece well enough that I can do an improvised solo while sightreading the chord changes.

I have sight-read the melody before, in a group setting - but that’s far more terrifying and less forgiving. I’ll only do that if it’s clearly a very straightforward or easy piece, like a ballad or showtune, with no surprises. If I do that I’ll deliberately take liberties and add flourishes so that anybody listening who knows the song doesn’t think I’m playing it incorrectly. Trying to play the notes on the page strictly means that if I make a single mistake, everyone will hear it. But if I pretend I’ve heard the piece a hundred times and have fun with it, then if I play a “wrong” note (but one that fits with the chord), it won’t sound like I don’t know the piece, it will sound like I’m just doing it a different way.

I hope that helps!

As a jazz beginner, I’d say one of the best things you could be doing right now would be to attend jam sessions. If you can find a good beginner-friendly jam session you should be able to play along with more experienced players and have a chance to occasionally play a solo or melody.