Cucumbers with dill are the most traditional pickle in the US, but nearly any vegetable and herb mixture will work. (Ripe tomatoes are too soft, and I wouldn't try raw potatoes, but we've had good success with every other veggie we've tried so far.)
Vegetables to fill the jar, chopped into similar-sized pieces if necessary (green beans and kohlrabi spears are two of our favorites)
1-4 cloves garlic (optional)
Herb or spice of choice (dill, cilantro, savory, mustard seed, cumin - whatever is in the fridge or sounds good!)
1 tablespoon non-iodized salt
~2 cups water (filtered if there's chlorine)
We use wide-mouth Ball jars for the majority of our pickles. Make sure the jar is clean, but it doesn't need to be sterilized. Pack the jar with veggies, herbs, and spices, leaving about 1 inch headroom. Mix water and salt and pour over to fill the jar. Place a clean smaller object (a jelly jar works great) on top to push the veggies under the brine. Cover with a piece of cheesecloth or a clean kitchen towel to keep bugs out. Really, that's it.
The amount of time it takes to ferment will depend on a number of factors: how fresh your vegetables are, how warm it is, and how sour you like your pickles. Start tasting after two or three days; when you like them, they're done! Move them into the fridge, where they'll keep for several months.
A little scum on top is totally normal; just skim it off. If any veggies float to the top and get moldy, remove them -- everything underneath is still fine. If the whole thing is slimy or smells bad, put it in the compost. (You probably didn't have enough salt.)