Have on the stove, simmering gently:
3+ cups of chicken or vegetable stock
In a heavy-bottomed soup pot or dutch oven, heat over medium-high heat:
2 tablespoons olive oil
1 tablespoon butter
When the foam from the butter begins to subside, add:
1 large onion, finely chopped
Once the onion softens and begins to turn translucent (about five minutes), stir in:
1-3 cloves of garlic, crushed (according to your tastes and your other ingredients)
1 cup of arborio rice
Stir and cook the mixture until the garlic is fragrant and the rice begins to release a nutty aroma, which should take less than five minutes – be careful not to let the garlic burn! Stir in:
1/2 cup of white wine or vermouth
Reduce heat to medium and stir until the rice absorbs the wine almost completely. For the rest of the cooking time, you will be adding the hot stock, one cup or so at a time, and stirring until the rice absorbs it before adding the next cup. How much stock you use really depends on how you like your risotto. I like it to have that signature creamy consistency, but retain a little of the bite of the rice, which usually takes about 10-15 minutes to achieve.
Once the rice is how you like it, you can add grated Parmesan cheese (about 1/2-3/4 cup, or more, if you like), which is the traditional. You can use other dry hard cheeses, too (asiago, romano, etc.), but softer cheeses will create a sort of gooey consistency, which is fine, if that is what you want. I can imagine using Gouda or Provolone and coming up with something a little over the top.
Regarding add-in vegetables, it depends on if they are cooked or fresh/frozen before you put them in; cooked can go in right with the cheese, but fresh and frozen vegetables should be added with the final few additions of stock so that they and the rice are ready at the same time.