So my basic recipe for vegetable soup is essentially "one diced onion, three chopped stalks of celery, two chopped carrots, and whatever else needs to get used up before it goes bad and will taste good in a soup."
I dice up and sautee the onion, celery, and carrots in a little bit of oil while I gather my spices (sage, parsley, paprika, chili powder, garlic, salt, bay leaves, and tamari/soy sauce are the spices I use the most). Then I start chopping up whatever veggies that need to get used (broccoli, tomatoes, zucchini, potatoes, more onions, spinach, cabbage, etc.) and add it to the pot, stirring frequently as I chop to make sure that nothing is burning. Once all my veggies are in, I'll figure out whether I'm making *just* vegetable soup, or if I want something more substantial. If it's *just* vegetable soup, I add spices to the pot and add water until all the vegetables are floating. Bring that to a boil, taste it, and adjust spices as needed. Reduce heat and simmer for at least an hour (tasting occasionally and adjusting spices; I recommend starting with a small amount of salt at first and adding as you go). When it tastes right, it's done. You can also choose to add pasta or rice during the last twenty minutes or so of cooking, just plop a cup or so of dry rice or pasta into the pot and let it cook, then taste and adjust for salt/spices again before you serve.
If I want something more substantial than just a vegetable soup, then once I've got the vegetables in the pot I'll add a pound of lentils or beans, then add water. At that point it's basically boiling and adjusting spices, periodically checking for tenderness in the lentils or beans (depends on if I've added dry or canned beans, and how long the beans were allowed to soak before I added them to the pot).
Dry lentils are a great thing to keep around because they're cheap, high in protein and fiber, don't need to be pre-soaked before you cook them, and basically never go bad.
If you've got stuff that won't taste good in your soup (maybe you don't want radishes in this soup but you've got radishes that are going bad) put those whole veggies in a bag in the freezer and when you've got a full gallon bag, take it out, dump it into a pot, boil it with water, strain the veggies out, and you've now got vegetable stock. You can also use things like the ends of carrots or potato peels or trimmings from onions or the tough parts of a tomato to put into your stock to add flavor and nutrition to it. Every time I cut an onion the ends go in my stock bag. You can use vegetable stock instead of water in your soup to make it more flavorful or nutritious.
If you want to experiment with flavor, you can try adding wine or peanut butter or vinegar or lemon juice or anything that sounds good to your soups. If you're vegetarian but not vegan, you can experiment with adding sour cream or yogurt or cream to your soups. For people who eat meat, any of the soup methods I've described here are very tasty with sausage or chicken added.