I don't use BTC-E, but most exchanges work like this:

1. Set up a wallet like CORE on your computer. It will take days to sync and will take up huge space on your computer. Make sure your computer is secure, wallets are computer files and are only as safe as your computer. DONE

2. Set up an account at an exchange in your country. Use real information. Because you are mixing dollars with BTC, when something goes wrong you will have less recourse if you are deceptive. DONE

3. Fund the account. You could link it to your bank account or use a money order, it depends on the options at your exchange. It takes days to weeks to move dollars, so there will be a wait. Once the funds are credited to your exchange account you can start buying. You can set a price you will pay, or pay the asking price. WAITING

4. Withdraw BTC to your wallet after buying. Your funds are secure once you have moved them to your wallet on your computer. Online wallets and exchanges come with a small chance that the owners will abscond with your BTC. It may be worth the risk for small amounts since wallet apps are so useful for cell phones. But for any substantial amount I would advise you to store that wallet offline.  WAITING