I've just been given my first Bonsai as a gift. Unfortunately the pot it came in does not have any drainage holes in it.
From what I've read it's important to choose the correct time to repot (eg when the roots have filled) so I just wanted to check the correct way to transfer my tree to a suitable pot asap.
Welcome to forum. In your case, if it is sure there are no holes, repot is urgent a must. Go for it after reading/watching a little about proper repotting.
Would you suggest I carry out all the steps outlined on the repotting steps on here, eg add new soil etc, or shall I literally just take out and pot the whole thing in the new pot?
Just transfer it into a container with drainage holes. Your aim should be to keep it healthy and alive for at least a year before doing anything drastic.