Today I painted a wall for the first time. I painted only one wall in a
bedroom and am not planning on painting the adjoining walls. I used
blue painters tape around all edges of the wall and when I pulled it
off, paint had seeped onto both adjoining walls and ceiling. It looks
awful. How can I fix it and how can I prevent it from happening when I
paint again?

It appears that you didn't burnish the edge of the blue tape down
before you painted.  If it isn't burnished then the paint will seep
under the tape.  This will happen also if the surface is rough. It
would probably be better to just hand "cut" (meaning just use a trim
brush) to define the line between the walls and the ceiling.  There are
paint pads that have rollers on them which allow you to paint tight to
corners also.  Just make sure the rollers are clean.

One method used by automobile painters is to use a clear coat of paint
to seal the tape and if anything seeps through it won't be seen after
the color coat is put on.  This method is rarely used in house painting.