The Indian lady who showed me how to make Daal didn't use onions and garlic as it was against her religion, but I use quite a lot of them.
Vegetables I always use:
Onion, garlic, coriander and tomato (fresh or tinned).
Other things I sometimes use if I have them in the fridge:
Celery, carrot, pumpkin, sweet potato, cauliflower, etc.
Cumin seeds and turmeric or premixed mild curry powder (approx 1tbs per 1 litre of daal)
The beans I use are Red lentils and Mung Dhall. Mung Dhall is what makes my Daal its unique texture. For 2 cups of lentils, 1 cup of mung dhall.
I cook the beans separately in plenty of water skimming foams off throughout the cooking process.
If using cumin seeds, heat the oil till quite hot. Drop a few cumin seeds and if they instantly froth, the oil is hot enough. Fry for a few seconds before adding the vegetables.
Add cooked beans to the vegetables including the cooking water.
Simmer until everything is nice and tender.