First thing you should do is roll towards the stairs because the Capra Demon will try take you out straight away. Before he can turn around try take out one of the dogs which should only be one or two hits with the Drake sword and then run up the stairs and get him to follow you. Keep using the stairs by running up and waiting for him to start coming up and then jump down the side. Once he drops down get a few hits and try learn his attack patterns. It's best at this point in the game to realise it's FAR better to dodge their attacks then to try block everything. Blocking never works out as you won't have enough stamina. I'd definitely recommend you try as hard as you can to do it without guides or videos though as it takes that feeling of accomplishment out of the game which it is really all about.