I am making a new game called, "Infinity Boy" and it will be my first game with sprites. It will be similar to Super Mario, so I need to know how to make a sprite "jump". Help would be appreciated.

I am assuming this is in either asm or axe right? If so I can help.

Nope. Its basic.

how are you doing sprites in basic, text sprites, pixel sprites, plot sprites, or hard coded sprites?

Maybe it's hybrid basic. In any case, making a sprite "jump" is as simple as redrawing the sprite up a certain number of pixels, then doing so again and again until you reach your max height, then dropping until you detect floor. This is best done with a loop of some kind, and realistic jumping (read: Slow in BASIC, and harder to make) has realistic gravity, which makes it so you fall faster the longer you are falling.

Considering that it's in the TI-BASIC subforum...

You may wish to track just position and direction, for constant-velocity rising and falling, or also track velocity to make variable-velocity, constant-acceleration jumping. The latter, as willrandship points out, is more accurate but slower.