One of the first things that I have found that is absolutely necessary in learning to solo is the memorization of the notes on the fretboard. With this knowledge you can play any scale quickly by starting at the root note, construct chords, and play solos.
Many guitarists begin soloing by playing pentatonic scale tones within the key of each chord as it changes within the progression. Many guitarists are content to remain in this "box" and are quite adept at its execution, such as ACDC's Angus Young and ZZ TOP's Billy Gibbons. Guitarists like Steve Vai, Joe Satriani, Yngwie Malmsteen and many others have become Modal masters and mastering these Modes creates a flavor that Pentatonic tones alone simply cannot compete with.
To start you should know your scale and scale tones and how they are applicable to the Major scale and the Modes as well. When we hear someone talk about a chord progression you have probably heard of the I, IV, V, I progression, it can also be numbered (1,4,5,1). In short, each interval, or tone has a number. For example we will use the C Major scale because it has no sharps or flats.
The C Major Scale is:
The scale is numbered as follows:
C=1, D=2, E=3, F=4, G=5, A=6, B=7, C=1
When the 2nd 1 is reached, you are now in the next octave of C.
Now a I,IV,V,I progression would be: C, F, G, and back to original C
Modes have a number as well, just as each tone of the major scale does. They are Major=1, Dorian=2, Phrygian=3, Lydian=4, Mixolydian=5, Aeolian=6, Locrian=7 and back to the Major for your 1.
So if you wanted to solo over your 1, 4, 5, 1 chord progression in C Major you would play the 1st position C Major scale over your 1 chord, 4th position F Lydian over your 4 chord, 5th position G Mixolydian over your 5 chord and back to 1st position C Major scale for your return to the 1 chord.
Now, the fingering patterns for each Mode works at all points along the fingerboard as long as you start at the appropriate root note of whichever Mode you are playing in. That said, here are the fingering patterns for each Mode. We will start in the key of F on the first fret to show how the tones ascend the fretboard. Remember that these fingerings DO NOT CHANGE only the Root Note "starting point".
F Major 1- 6E 1,3,5 5A 1,3,5 4D 2,3,5 3G 2,3,5 2B 3,5,6 1E 3,5,6
G Dorian 2- 6E 3,5,6 5A 3,5,7 4D 3,5,7 3G 3,5,7 2B 5,6,8 1E 5,6,8
A Phrygian 3- 6E 5,6,8 5A 5,7,8 4D 5,7,8 3G 5,7,9 2B 6,8,10 1E 6,8,10
Bb Lydian 4- 6E 6,8,10 5A 7,8,10 4D 7,8,10 3G 7,9,10 2B 8,10,11 1E 8,10,12
C Mixolydian 5- 6E 8,10,12 5A 8,10,12 4D 8,10,12 3G 9,10,12 2B 10,11,13 1E 10,12,13
D Aeolian 6 - 6E 10,12,13 5A 10,12,13 4D 10,12,14 3G 10,12,14 2B 11,13,15 1E 12,13,15
E Locrian 7 - 6E 12,13,15 5A 12,13,15 4D 12,14,15 3G 12,14,15 2B 13,15,17 1E 13,15,17
Finally, for the aforementioned chord progression, using the above fingerings for each mode you would play C Major Mode with the root note beginning on the 6E 8th fret, the F Lydian Mode with the root on the 6E 13th fret, the G Mixolydian Mode with the root on the 6E 15th fret and return to the C Major Mode with the root on the 6E 8th fret.
These rules can be applied to any Major key and I will include these last few examples in closing:
Key of D Major D E F# G A B C# D
Chord Progression D, F#, G, A, D
Solo D Major, F# Phrygian, G Lydian, A Mixolydian, D Major
Key of E Major E F# Ab A B C# D# E
Chord Progression E, B, C#, A, E
Solo E Major, B Mixolydian, C# Aeolian, A Lydian, E Major
This is very simple and as long as you count your scale tone numbers and use the appropriate Mode numbers this is a very effective way to improvise solos.