[Hazella]

It looks pretty straightforward! Just take it one step at a time. Ikea furniture is generally pretty easy to put together, particularly something small like the Billy shelf extension. I have assembled Ikea furniture before and have found a rubber mallet to be handy, gentle taps can help push pieces together. With only three pieces though your hands should be enough!

You could even add silicone along the inner edges where the wood meets to strengthen the connections and keep gunk from building up in the corners/edges for easier cleaning.

With cutting the wood pieces for the top door, just be sure to check your measurements and you should be fine. The store which you purchase the wood strips might even be able to cut them for you (here in the US the big corporate home renovation stores do so, I don't know about in the UK).

Also make sure the nails you use are are not longer then the width of the wood you use for the door or they can poke through the wood on the opposite side; a staple gun would be easier if you have access to one. I remember making that mistake on one of my first woodworking projects and had to start all over!

Good luck on your project! If you can, post some photos when you are all finished, I'd love to see how it turned out!