Actually, E is the 5th of A

There are so many ways to do this. Say you are in C
From C to Db use an Ab7 from out of C into Db, just as you would use an A7 into d

From C to Eb. go from C major, to F minor 7 to Bb7 to Eb. you're just going in the circle of 4ths from C to Eb

From C to E. This one is a little tricky. go from C down a half to B7 and into E. Sound better if you use a B suspended 4th, then resolve. if you use the B sus chord, you will share the E note in both chords. A C chord is of course C E G. A B sus7 chord would be B E F# and A. Sharing the E in both chords will make it sound better since you are transitioning to E anyway.

From C to F. just use a C7 coming out of C into F. or a Gmin7 will sound good before the C7

from C to F#. Go from C to C#7 into F#. A nice half step transition from C to C# and into F#

from C to G. this one is simple.

From C to Ab. another tricky one. No terrific ideas, but these do work. Go from C to A min, up a half into BBmin, and into Eb7 and finally into Ab. or you can just use a C chord, with C on both sides CEGC. then move your bass down to Bb, still maintaining the C chord in the right hand, and then moving the bass into Ab, while changing your right hand chord from CEGC to C Eb Ab C. Now you are in Ab

From C to A. from C, move bass up to E, which is the 3rd of the c chord. then keep bass in E, and use a suspended E chord in right hand, E A and B, or a variation thereof. OR you can do the half step down from C into Bmin to E7 to A

from C to Bb. Simple circle of fifths. from C to Cmin to F7 to Bb. or skip Cmin altogether if you want.

and from C to B. you can go from C to C#min to F#7 to B. or from C to F to F#7 to B.

These are a few examples. even more when transitioning from major to minor. Some sound better than other, and some keys just don't transition well. The smartest thing is to use half steps, whole steps and the circle of 4ths and 5ths. experiment with going up a tep, then down a fifth. up a fourth and up another half step. as you watch my examples this is what I do. use as many 2 5 1 progressions and half step or whole step modulations as possible.

Hope this helps somewhat