Read up on what you can do to prepare the garden bed. Adding compost is a must in my opinion.
Since you are gardening for the first time, I'd like to suggest that you start with plants that are least likely to give you trouble.
Eggplant,cucumber,tomato,cauliflower,cabbage,watermellon,peas,carrot, beet,onion
Out of these, I would say,
cucumber is the easiest. Put up a 5~6 foot high net trellis in the back (north side) of your garden bed so the cucumber vines can climb up.
I might be wrong, but I suspect that it's a little late for you to start
peas now but that would be my next pick. You can plant the peas this fall after the weather cools down. By that time, you might feel more confident to also plant the other cool weather crops: cauliflower, cabbage, onion, and beets. They can replace the warm weather crops that would be winding down or are already harvested.
At this point, I'm inclined to recommend
tomatoes. And even though starting indoors is the norm for me because I have to get a head start here in New Jersey, I wonder if it might be possible for you to just directly sow the seeds in the ground right now. Success will depend on which variety tomato seeds you have. Some fruit as early as 50~60 days, some take as much as 80 days. If you get into hot weather, tomatoes will stop fruiting.
Tomatoes will need about 24"x24" space so that's going to take a big chunk out of your available garden space. Plant it in the back, but away from where you planted the cucumber.
Eggplants, I also start early indoors, but they are relatively easy starters -- especially Asian eggplants which are early to fruit as well. You might also try planting these seeds directly in the garden. At least 18"x18" space.
Carrots take a little more care because they take longer to germinate and you need to keep the soil moist until they do. They also take a while to mature, but they're great fun. They need
deep fluffy/loose somewhat sandy soil. It's usually better to pile the soil up higher. Sow them on the top surface,
lightly cover with sand mixed with soil, then scatter some
dried grass clippings on top as mulch to help keep in the moisture. You should still be able to see the ground. Carrot seedlings have a pair of thin leaves. When you see them sprouting, you may need to remove the grass clippings to help them grow up.
OK, I left the watermelon till the end because they take up a LOT of space. It's not hard to grow, but it would be about the only thing you'll be able to grow in a small space.
You didn't mention
beans, but they're just about the easiest things to grow. Don't you like beans? You'll be surprised how much better home grown beans taste. You can grow pole beans on the trellis, and bush beans can be pretty closely spaced depending on how well your garden bed is prepared. I grew Purple Podded Pole beans and yellow podded Marvel of Venice Pole beans last year, along with Jade Green Bush beans.
For greens,
Swiss Chard is very easy to grow, and you can get a variety mixtures called Rainbow Chard or Bright Lights that have leaf stems ranging from dark red, pink, orange, yellow, and white. The leaves are good in salad when small and cooks up like spinach when big.
Have fun and good luck. Come back with any questions you might have.
I am all excited !!
The Los Angeles area (from San Fernando down to Long Beach, and from the coast eastward to Claremont) contains 
