Memorize the keys of the E scale until you don't need any notes or reminders. This is particularly useful for improvising and songwriting because playing the keys from memory makes it easier to experiment with different structures and styles. Play the scales in ascending and descending orders to get a feel for the sound and pitch of each note. The scale of E major is E, F#, G#, A, B, C#, D# and E and the scale of E minor is E, F#, G, A, B, C, D and E.
Play the keys again and try to find out which notes sound more harmonious together. Doing so will help you discover patterns in the notes that you can use in your songwriting or improvised solos. Play, for example, the F# and C# notes of the E minor scale and you should notice how they complement each other's sound and pitch. Experiment with other notes and look out for more pitch harmonies - this should help you with ideas for writing and playing.
Look out any notes that sound like a particular style of music. The key of E is often used for jazz and blues but you might find other notes that suit your preferred style (e.g. rock or progressive). Play the E, G, B and top E notes of the E major scale in order and you should hear a very classical and smooth sound coming from the instrument. This is actually known as an arpeggio and is often used in classical music.
Use chords to add more texture and harmony to your playing. Chords are a great way to provide bravado and drama to a piece of music because they sound so bold. They also let you move away from the linear sound of a set of notes played one after another. For example, play the E, G and B notes of the E major scale to create a triad chord of E. Or try playing the A, C and top E of the E major scale to make another in A.
Always play with good technique. No matter what instrument you play with, making sure you play with the correct technique should help you improve your skills as a player in general. Piano players, for example, should sit up straight and have their fingers in a naturally curved shape. Bass players, on the other hand, should strike the strings with enough force to produce a clear and non-muffled tone. Your fingering should also be precise for any instrument.
Experiment with the different notes, chords, sequences and melodies to master the key of E. You might try to focus on one style of music such as jazz or blues or you could just keep playing away until you find something relevant for a personal song.