Please use strictly according to the instructions.

Literal

To-the-very-end instruction-manual [according to-に従って] honorific-use-please.

A stock line from product manuals and safety warnings. あくまで (or あくまでも) literally 'to the very end' means 'strictly', 'without exception', 'absolutely' — it emphasizes uncompromising adherence. お使いください is the keigo template お + verb-stem + ください, a polite request form more elevated than plain ~てください.