How can i level up and get lots of caps just after leaving the vault in fallout 3

There aren't any real get-rich-quick schemes short of actually playing the game, although there are a few things to keep in mind.

1. Selling enemy-dropped equipment and weapons can get pretty profitable. Assuming you've invested some points in Repair, this is a great way to make money. Be sure to keep a Utility uniform from Vault 101 as you will not find any +Repair items for a long time afterwards. This also helps by lessening the need to use repair services from vendors. Raiders at Super Mart and Springvale School drop a ton of stuff.

2. Quests pay out really well. In conjunction with doing quests like Moira's Wasteland Survival Guide quests to the Super Mart (tons of items and enemy drops), or Minefield (walk around disarming and collecting mines for 25 caps each). In addition to the cash gained from scavenging and looting, you get items and rewards from the quests themselves.

3. Your Barter skill will increase the money you receive for items and lower the costs of purchases. When dealing with vendors, wear +Barter or +Charisma gear to maximize cash back. Beer will also increase your Charisma by 1 point. Any other form of booze is worth more to you as something to sell. Early items that increase these skills are Lucas Simms' hat (+1 Charisma), or if you manage to kill any wandering merchants, they tend to wear +5 Barter coats and hats. Additionally, know where to sell. If you're nice to Gob in Moriarty's, he'll give you a significant discount and buy things at a much higher price than any other vendor early in the game. (Remember, it never pays to discriminate, kids.)

4. If you've focused on Luck (5 Luck or more) and can wait until Level 6, you can get the Fortune Finder perk, which lets you find more caps in random containers. Arguably better is Scrounger at level 8, which lets you find more ammunition, including rare ammunition. All ammo is weightless, so you can stockpile all of it and sell it when needed for a tidy profit.