Beardies are omnivores. As a hatchling they start off 80% - 100% insects, and gradually go to 75%-80% greens/veggies and 20%-25% insects. As babies they should be offered insects 3 times a day, after around 4 months twice a day, after around 6-8 months, or after their last big growth spurt once a day. Then down to a few times a week. Good insects for primary feeders are crickets, Phoenix worms, and silkworms. Superworms are good for adults. For treats butterworms are great, and waxworms & hornworms are good too. Mealworms should be completely avoided for babies, they are almost all shell, and the chitin can be hard to digest. And they are very low in nutrition, so they have to eat allot to get anything out of them when they are growing, which requires allot more shell, so the problem gets compounded.
A salad should be offered every day, preferably in the morning. Babies may ignore it entirely, by the time they 8-10 months old they should be eating greens everyday. Each dragon is different, and they can be picky. Most regular lettuces should be avoided, they contain very little vitamins or minerals, especially iceberg. The majority of the salad should be denser, dark greens high in calcium and other minerals. Collard greens, mustard greens, dandelion greens, and turnip greens are generally the best commonly available. Escarole and endive are good too. And mix in different good veggies. Butternut squash s generally a favorite of almost all dragons, and is good in vitamins. Either steam it lightly, though I don't think this is as good, or mince or grate it. Variety is good, as you are getting different nutrients, and it helps keep the dragon from getting bored. Avoid feeding allot of vitamins that are high in vitamin a, and avoid feeding allot of greens and veggies that are high in oxalate's, as this binds to calcium and inhibits proper absorption.
Fruits can be added, I do normally a few times a week. I try to go for fruits high in calcium, like papaya. Avoid acidic fruits, as their stomachs can't handle allot of it properly. Citrus, pineapple, tomatoes, etc...
For supplements, calcium is the big one. The ideal calcium:phosphorus ratio is 2:1, and most insects are far below this, so it is especially important for babies that are growing and eating allot of protein. Phoenix worms are high in calcium so they don't need as much supplementation. Butterworms are also very high in calcium, but most people, including me, think they are high in fat. So I wouldn't use them as a staple feeder. Typically you want to dust one insect feeding a day with the calcium for babies. For adults I do 2-3 times a week, but I also go out of my way to make sure they are eating calcium rich foods. The type of calcium that is best is up for debate as well. Some contain d3, and some don't. And the amount of d3 also varies quite a bit. A dragon should have a high output UVB bulb, and manufacture it's own d3 that way. I use a calcium powder with very low d3. You should also use a reptile multivitamin. There are 1000's of opinions on which are the best. And the common idea is to use it once a week instead of the calcium. I typically add a little bit to the calcium every other time.
The beautiful dragons nutrition page is a great resource, the woman who runs the site has put allot of time and effort into collecting nutritional information and dragon health information. I would say this chart is a must read for any bearded dragon owner.