We begin our scale studies with an E Major scale on the first string. Play the scale up & down, as written. Use a pick, your thumb, or other finger to set the string in motion. Use any fretting fingers (there are many options - see challenge below). Space the tones evenly, in 8th notes (1 &). This will be easier once you determine the best positions/shifts. Starting from an open string, we can clearly see the 221-2221 pattern in frets [gray numbers between fret numbers below].
The ♯ [sharp] raises a tone 1 half step. Since fret 1 on the first string is an F, fret 2 is called F♯.
These tones [below the fret numbers above] make up the key of E Major. A key is the set of tones which are the basis of a melody, a song or part of a song.
This type of scale (Major) can be played on any string...we'd have the same key on string 6 (E Major), And, A Major, D Major, G Major, & B Major on strings 5, 4, 3, & 2, respectively. And, if we moved all of these tones up one fret (start pattern at fret 2), low to high, we'd have F Major, B♭ Major, E♭ Major, A♭ Major, C Major, and F Major. Push it up one more fret, low to high, and we have F♯/G♭ Major, B Major, E Major, A Major, D♭ Major, and F♯/G♭ Major. That's all of them for linear versions.
Design your position strategy. Make decisions and put them to work. Try more than one scheme. Even if you don't want to do this, do it. Every time we put this level of focus on the simple, our playing system is upgraded, even if results show up days or weeks later. Consider: we always want to know what position our fretting hand is located. This is a mind and a feel type scenario - we will want to close our eyes at times. Think it through now, so the body can take over while in jam mode. For this scale, we have a lot of options, since we have to shift.
Before you look below, figure out your own solution or solutions.
Here are two options (fingerings are below the fret numbers)...