Re the laws.
First off there's a scoreboard to keep you up to date.
Second, have a look at James Trollope's The Bluffer's Guide to Cricket: Bluff Your Way in Cricket (The Bluffer's Guides) which is £1.15 at Amazon for Kindle.
Look at the diagrams
Umpire's Signals often if a review is called for there's a wait and then a cheer or groan, depending when the Umpire signals someone's Out.
You probably only really need the six on the left hand side.
Fielding Positions
Listening to the commentary can sound like a completely foreign language, so I restrict myself to understanding the slips, the gully, short leg, square leg, mid and deep wicket. But really it's just to give an indication to the listener where the ball's gone.
Don't mention The Ashes, due to be played over here later this year, because that's a competition between England and Australia only. The New Zealand matches are less confrontational (I think it's fair to say that) a bit better natured. The NZ team is known as the Black Caps.
It's very civilised, the cricket, quite an emphasis on hospitality, drinks break, lunch, tea and so the clothes are smart but comfortable, as befits an all day event really, yes, much like the tennis.
Have a great time.