Well, the failure of the first was because Budapest didn't try to move (it issued a suport move instead). The failure of the second was the same. You should have issued one of them to move, and the other to support it.
http://www.wizards.com/avalonhill/rules/diplomacy.pdf is the official rules for the game of Diplomacy and should answer most of your questions about the basics. The rest of the posters here on the forum (myself included) will be happy to help with the more esoteric issues. One thing to note: keep questions in as generic a form as possible if about an ongoing game, and never ever reference an ongoing game by putting a link to it on the forum. This is considered bad form.
Some things in general:
Gunboat = this is a game with NO textual communication (no chats, nothing on the forums, no PMs).
Public/Global Press Only = Only press that every one can see is allowed. This may be in game (usually, nowadays) or here on the forum (some oldschool games use the forum before the days of the chat log).
Anonymous = You won't know who the other players are and it is frowned upon to try and figure it out for the purposes or metagaming. although some variants, the fun is in guessing who the other players are.
Common screwups by noobs.
Support hold can only support a unit not attmepting to move. Convoying, holding, support move, and supporting hold are all hold orders and the unit in question can be support held. Issuing a move order, even if it fails, will break the support and leave the unit vulnerable.
Support move must refer to a moving unit.
Read the manual and ask more questions to your hearts content.