C major scale fretboard
A simple way of looking at this guitar scale picture.
An easier way to look at these guitar scale patterns is to make 3 patterns instead of 5. This may help you in the beginning to at least get it into your memory.

At the end of the day though, It's important to familiarize yourself with the whole group of interlocking scale patterns.

The simplified version is pattern 1, pattern 3, and pattern 5.
The fifth scale pattern will still interlock with the first pattern (octave) though, so there's no getting away from that.

The C major scale full fretboard

How this C Major scale guitar fretboard diagram works.
Working out how to get these major scale patterns onto a fretboard created a few minor challenges for me, mostly because every one of these fingering patterns shares half of the notes in the preceding pattern.

You'll see here that there are five patterns.
All of the notes that have yellow in them are the first pattern, and those that have red in them are the second pattern and so on, but because they all share notes, I've had to use two colors.

5 Lead guitar patterns in the C major scale

Here then are the fingers you should use to play these scale patterns.
If you find yourself using other fingers to play certain notes, as long as it works for you, don't feel like you're doing something wrong.

These finger positions are based on the 1 fret per finger rule, but a lot of the time it depends where you've just come from on the fretboard.

Here's a picture of what the different finger numbers are, followed by all 5 scale patterns and a 6th pattern which is the octave of the first, so you can get the fingering right for other keys as well.
C major scale on guitar - First position with finger numbers
C major scale on guitar - second position with finger numbers
C major scale on guitar - third position with finger numbers
C major scale on guitar - fourth position with finger numbers
C major scale on guitar - fifth position with finger numbers
C major scale on guitar - 6th position with finger numbers

How to pick these major scale lead patterns

A good way to practice picking guitar scales is with alternate picking.
All this means is that you pick the first note with a down stroke, the second note with an up stroke, the third with a down stroke, and so on.

I used to practice these scale patterns, going from the lowest note to the highest and back again.

While you might not necessarily use them that way in a solo, it helps you memorize them, and it's a great finger and picking exercize
Where learning all 5 lead guitar patterns will come in handy.
When you begin to use these patterns to play lead guitar over various chords, you'll start to notice that each pattern starts on a different note, and that note is sometimes the root note of the chord it works best over.

In the first pattern you'll see how a C chord fits nicely into it. By playing between the notes that make up a C chord you'll hear how emphasizing those notes in the pattern help create a meaningful and melodic solo.

You'll also start to see extra patterns that fit best, like for instance if you're playing in the key of C over an F chord.

When playing lead guitar over an F chord, the scale pattern can be an extension of the 2nd pattern by starting at the first fret. The last note on the first string in the second position pattern is of course one too many for an F chord

Experiment with what works best for you. When playing lead guitar, I like to use the notes that make up the chord I'm playing over as a foundation for the melody.
It has to resolve nicely into the chord, especially at the end of the guitar solo.

Once you've familiarized yourself with these 5 patterns, practice moving from one pattern to the next one along, both the preceding and following pattern. You can use a different string each time as an exit point to the next position.

This is where lead guitar playing becomes interesting.

Another thing I practiced quite a lot in the beginning was running down one string all the way along the fretboard and then using different points to jump off into one of the major patterns.

Have fun. There's a lot to do here with the major scale if you put your mind to it.

Another thing you may want to do, is to record some rhythm guitar progressions that repeat often enough so you can practice soloing over them.
The Electric Guitar

How to tune the Guitar

How to use a Plectrum

Beginner Guitar Chords

How to play Barre Chords

How to play Power Chords

Guitar Scales

The C major scale on Guitar

The Pentatonic Scale on Guitar