Hi.
First, there is a fantastic tutorial in the single player and options menus, which goes through literally everything.
in terms of the field, imagine it like this.
at the bottom and top are you and your opponent's hand. Naturally you can't see their hand contents unless you use a card that let's you do so.
going up from your hand you have the five spell and trap zones, which pendulum monsters are also placed in. on the left hand side of this is your extra deck, so you can view and special summon Fusion, synchro, XYZ and link monsters. Note that the card XYZ dragon cannon is not a XYZ monster.
above you have your monster zones. you have five main ones, and 1 extra one which link monsters are placed when you summon them.
You used to have to summon a link monster and other extra monster zone monsters here, but now you can summon as many extra deck monsters as you like again with the new rules introduced.
to the left of your monster zones are where your field spell is placed, and on the right is your graveyard or G.Y and bannished/removed from play cards.
I recommend looking up the yugioh wiki for a better explanation.
to access your graveyard, press y on it, go down once and press a to enter to see what is in there. same with your opponents.
As for keeping up, that's where the card prompts as for whether or not you want to use them are actually helpful for us, as they pause the game and let us see what is placed.
So you'll never have a time when you can't react to something with a card of your own.
Hope this helps.
oh and one more thing, I'd recommend looking up the yugioh card database to search info for cards if you need it, as well as
thecardhub.net which will tell you where to find cards in the packs in the game.