The basic equipment you need is a wand blender, a big saucepan, a chopping board, a wooden spoon and a good knife.
Basic process for a smooth soup: I always start any soup by frying onions slowly in a bit of vegetable oil, usually garlic as well added at the end. Then add whatever veg you like, and stock. I use a Knorr vegetable, chicken or ham cube. Some people make their own stock. You want a bit more liquid than you generally need for boiling vegetables. Bring them to a boil, then simmer.
Don't overcook the veg. Peas only need about 5 minutes. Tomatoes about ten. Brassicas 10-15 minutes. Carrots 20 ish. Potatoes 20-25
Good combinations: Potato and leek, broccoli and Stilton, pea and ham, carrot and coriander, "casserole/stew mix" from Aldi, Sainsbury's etc (Aldi also do a Soup mix of ready chopped veg which is souper easy- sorry!). Spiced lentil, curried parsnip or cauliflower. Add cooked ham towards the end of the cooking time, for the last minute if it's pea and ham.
When cooked, turn off the heat. Blitz with the wand until smooth. Taste it. Add the Stilton now and melt it in if you are doing broccoli and Stilton soup. Add the curry powder or herbs if using. Add plenty of pepper and a bit of salt (not very much salt if ham or salty cheese are involved). Adjust it until the seasoning is right. Put it back on the heat and simmer for a couple of minutes.
Toppings: Tomato soup must have grated cheese on it. Most of the vegetable ones are lovely with chilli flakes in and/ or cooked crispy bacon chopped up into little bits.
Serve with crusty fresh bread and proper butter.