I find solo arrangements one of the most enjoyable things you can play on the guitar. It is just great to be able to sit down and create complete music on your own. Unfortunately, solo guitar is difficult to get good at technically, and it is particularly hard in the beginning. There is no standard approach you can apply, as with the piano where you can play the chords with the left hand and the melody with the right. Start working on simple arrangements, and with time you will acquire the skill necessary to play the more advanced arrangements.
Here are three pieces of advice that I feel very strongly about.
Keep time. When you are rehearsing a solo arrangement and you have got to the stage where you know how to play a few bars, in the sense that you know what your fingers are supposed to do, make sure you practice in time. Don't worry about playing in super slow-motion, the tempo does not matter. What matters is that you keep the flow. Use a metronome or a click track regularly so that you won't be able to cheat, which can easily happen even if you are in good faith. Solo arrangements are rarely difficult because they are fast, rather they are difficult because the fingerings are complex. Once you can play an arrangement slowly, in time, it is usually reasonably quick (and fun!) to work it up to performance speed.
Move your fingers only when you have to! You frequently have to let several notes ring at the same time and, similarly, you frequently have to play several notes simultaneously. Be economic with which fingers you move, and when. You need to get beyond the application of 'chord grips' as they are used in strumming. Have a look at the example shown on the right. In bar one, there are two inversions of Dmin7, the first falling on beat one and the second on beat three. If you were to repeat bar one a few times you are effectively playing chords, and you have to change the fingering of all four notes at the same time when you switch between the two chords. It requires a quick adjustment. Now consider bar two. After fretting the first note on beat one, you have time until beat two to fret the other three notes. The same goes for the second chord. You have time until beat four to fret the three notes after playing a single note on beat three. The notes in the two bars make up the same two chords and uses the same fingerings so it is tempting to employ the same left-hand mechanics in both cases. However, bar two is easier to play than bar one and it also sounds more fluent in a solo arrangement. Be aware how long you have to fret the notes, particularly when they make up a chord that is familiar to you. Don't go for the all-notes-at-once approach unless it is strictly necessary.
Record yourself. You absolutely have to record yourself occasionally. Things just don't sound the same when you playing and when you are listening. It is partly physical, I think; some things are just more fun to play than others, and that biases your judgement. In addition, I also find that small details sometimes make a big difference. For example, whether you play a chord on the beat, or just before the beat, can change the feel of a passage completely. Above all a recording will make any problems with your time-keeping painfully obvious.
You should also think about how you want to use your right hand. Do you prefer to play with the pick only, or do you like plucking the strings with your fingers? I don't want to try to sell you a specific right hand technique because I think it is a personal choice. If you keep an open mind and experiment occasionally you avoid getting stuck with bad habits, and you should be able to keep improving.