You will need a pin and/or a small craft knife to remove the old button material. For the new buttons, all you need to do is remove the sprues, clean up the edges with a fingernail, nail file or fine sandpaper, and glue them on. When handling the new buttons, please be gentle as the material is brittle, and the button plates will snap if they bend.
The plates and buttons are translucent, but can be painted. There's a tutorial on how to clean and paint this material here.
Please note that due to the nature of this design, the watch will no longer be waterproof.
You might also want to test out your chosen glue on the small bar piece which you won't be using, before you glue the plates to the case. Silicone craft glue applied in a fine layer works well. Superglue will also work well, but you might want to use "slow" superglue!