A black jack basic strategy for online casino gambling is not going to vary from a strategy you would bring with you to Vegas. The game is the same; therefore the strategies are going to also be the same. If you know how to play casino then you should have no problem converting your game to an internet casino.
Approaching a strategy requires a lot of thought as well as consistency. There are different books out that will tell you different things. But, there is no proven winner in this game of luck and skill. The best advice that you can take is to incorporate all of the common strategies across the board.
For example, a common strategy is to stand on any hand that could bust when the dealer has a 4, 5 or 6 showing. The dealer is going to have to hit no matter what. This strategy will make is so that the dealer takes the bust card rather than you. If you have a hand that you cannot bust on, then double down. Even if you get a bad draw, you are still banking on the dealer busting.
Other tips include watching the cards. Counting is not legal and not easy in any blackjack, but being aware of the cards in play is always helpful. If you have noticed a lot of big cards in play recently, chances are good that the next cards out will be smaller. These are simple strategies that will keep you aware of your surroundings and in the game.