Most kind! 
Hi, I’m a retired chess teacher and have an international rating.
a) Memorising openings is wrong at every level (even Grandmasters don’t do it. 
)
This is because:
- you want to understand openings, so you can react well when your opponent plays an unexpected move
- there is a massive amount to ‘remember’
- there are much better ways to spend your valuable time
b) Chronos is on the right lines with sticking to principles in the opening.
Assuming your opponent is not threatening anything with their latest move (always worth checking!), you should try to:
- control + occupy the centre (it’s the most important part of the board)
- develop your pieces (i.e. bring them out to attack more squares)
- get castled
To explain each of the above in more detail:
- the centre is defined as e4, e5, d5 + d4. It’s important because from any of those squares you can quickly reach any other part of the board. And if you control the centre, your opponent’s pieces have to go the long way round to get anywhere.
- on g1, the White Knight controls e2, f3 + h3 (=3). By playing Nf3, the piece now controls g1, e1, d2, d4. e5, g5, h4 + h2 (=8)
- after a sequence like e4 … Nf3 … Bc4 … OO, your King is safely tucked away and your rook has come into play
c) Next it is a good idea to learn about tactics. (Tactics are things like pin, fork, skewer, overload and discovered check.)
Tactics are fun to play; crop up quite a lot and are relatively easy to learn. 
Here are two examples:
- e4. d6 2. d4 Qd7 3. Nc3 Qc6?? 4. Bb5 (this pin wins a Queen for a bishop)
- Nc3 d5 2. d3 e5 3. Be3? d4 (this fork wins a piece for a pawn)
If you get a book on tactics (or use the Internet), then play through lots of tactics, you will come to spot patterns - which is a huge part of playing chess well.
d) I think an important way for players of your strength to improve is to study endings (particularly basic checkmates.)
This may seem odd, since the ending is a long way away from the start!
But here’s the thing - endings are great to study because:
- there’s only a few pieces on the board, so it’s much easier than openings
- you can usually see if you are making progress
- once you learn the correct way, you can use it forever
- it avoids the frustration of being ahead on material, but unable to win
You should master these checkmates:
- K+Q v K
- K+R+R v K
- K+R v K
- K+B+B v K
Not only do they come up, but you will gain confidence and learn to plan ahead.
e) Finally you should play games.
A friend about your standard is jolly useful; a computer program is very convenient.
OK, that’s a good start.
Now (if you’re interested) I have played practice games right here on the SDMB.
We have two threads - one of the game (in which I will offer to let you take back blunders 
) and one for comments and analysis.
Here’s such a game: Chess: glee v Mosier - The Game Room - Straight Dope Message Board
and the accompanying thread: Chess: glee v Mosier comments - The Game Room - Straight Dope Message Board