To Give
To Raise Up
transitive verb, ichidan verb
This is a really humble and polite way to say "to give," probably because you're lowering yourself down and raising the item above your head so far that you have to point at it because if you were touching it you'd be defiling it anyways so, you know, point at it and raise it way up, you little worm on the ground.
The reading is 差す and 上げる put together, both hopefully words you know okay by now.
パソコンの動作を速くするのに役立つアプリケーションを無料で差し上げます。
I’ll give you this application that helps make your computer run faster for free.