This is mostly for @Ominous but I figured I'd make a forum topic on it for everyone to see because you know he/she can't be the only one for whom this is helpful.
Basically, the place to start is knowing your chord families and scales. So let's take for example the key of C. You have the C major scale (C D E F G A B C) which gives you the basic triads C, Dm, Em, F, G, Am and Bdim for example.
An arpeggio really is a broken chord so you play each of the notes in the chord separately. I.e.
C - C E G
Dm - D F A
Em - E G B
F - F A C
G - G B D
Am - A C E
B - B F D
How to use these in a solo it really in it's most basic ways by playing the arpeggio over the chord so C arpeggio over a C chord, Dm arpeggio over a Dm etc.
However, that's a little bit boring so to add some spice to it you my want to start on the E instead of the C(one of my favorites) or start on the G instead of the C when you play over the C. But that's still faulty basic. You can also add notes, for example you can play Cmaj9(add a D(and B)) Cmaj7(add a B), Csus2(replace the E for a D), Csus4(replace the E for an F), Cmaj11(add an F(and B)) arpeggios over a C. You can even play a relative minor arpeggio over the major chord(or relative major over the minor) which in this case would be Am over the C making it more resembling of a C6 arpeggio and is another one I like to use sometimes.
For scales what you really want to try to do is use the scales that you know fit over the chord or the whole chord progression. A scale effectively is a collection of notes you know work over a chord (progression)(some sound better to and on than others but overall each note gives a certain vibe) and that's how you can decide which one you want to use. It can be any of the major modes over a C major chord for example. The most important aspect would be to not just play the scale up and down because nobody wants to hear you practice a scale when you play a solo(we do want to hear you practice a scale on the school tho). Try to be melodic, create a motif, skip notes every once in a while etc.
I figured I'd not go too deep, if you have any questions feel free to ask!
Basically, the place to start is knowing your chord families and scales. So let's take for example the key of C. You have the C major scale (C D E F G A B C) which gives you the basic triads C, Dm, Em, F, G, Am and Bdim for example.
An arpeggio really is a broken chord so you play each of the notes in the chord separately. I.e.
C - C E G
Dm - D F A
Em - E G B
F - F A C
G - G B D
Am - A C E
B - B F D
How to use these in a solo it really in it's most basic ways by playing the arpeggio over the chord so C arpeggio over a C chord, Dm arpeggio over a Dm etc.
However, that's a little bit boring so to add some spice to it you my want to start on the E instead of the C(one of my favorites) or start on the G instead of the C when you play over the C. But that's still faulty basic. You can also add notes, for example you can play Cmaj9(add a D(and B)) Cmaj7(add a B), Csus2(replace the E for a D), Csus4(replace the E for an F), Cmaj11(add an F(and B)) arpeggios over a C. You can even play a relative minor arpeggio over the major chord(or relative major over the minor) which in this case would be Am over the C making it more resembling of a C6 arpeggio and is another one I like to use sometimes.
For scales what you really want to try to do is use the scales that you know fit over the chord or the whole chord progression. A scale effectively is a collection of notes you know work over a chord (progression)(some sound better to and on than others but overall each note gives a certain vibe) and that's how you can decide which one you want to use. It can be any of the major modes over a C major chord for example. The most important aspect would be to not just play the scale up and down because nobody wants to hear you practice a scale when you play a solo(we do want to hear you practice a scale on the school tho). Try to be melodic, create a motif, skip notes every once in a while etc.
I figured I'd not go too deep, if you have any questions feel free to ask!