The answer varies from snake to snake. Most venomous snakes have special antibodies that make them immune to their own venom, though some are not. This immunity can range from full immunity to the venom of any snake of their species to a partial immunity to just their own personal venom. This is similar to the human body. For example when you transplant an organ from one person to another the recipient's immune system recognizes that the transplanted organ is not theirs and will attack it, a process known as "rejection," unless the recipient takes drugs that suppress their immune system. Similarly a snake's immune system can tell which venom comes from that particular snake, and in some instances can fights it off so effectively that there is no impact whatsoever.

Snakes avoid getting their own venom into themselves based upon which fang structure they have.

Vipers like the Diamondback Rattlesnake are known as solenoglyphous snakes. If you look at the first picture you can see that there is flesh and muscles around the fang of a viper. In the second image, which shows the skull of a Diamondback Rattlesnake, you can see that there is a hinge attaching the fang to the jaw. These kinds of snakes are able to fold their fangs against the inside of their mouth when they are not in use to avoid biting accidentally or biting themselves. You can also see how the fangs are curved, so they wouldn't bite the jaw of the snake even if extended. These fangs can be up to two inches long.

Proteroglyphous snakes, such as King Cobras, Coral Snakes, and Black Mambas have fixed fangs which cannot fold up. These snakes have shorter fangs that cannot reach the bottom of their mouth so they cannot accidentally bite themselves. They are also curved a bit for that same reason.

Opisthoglyphous snakes, such as the Boomslang, have fangs which are located towards the back of their mouth rather than up front. This means that they have to get a good hold of something to inject venom. Most rear-fanged snakes are relatively harmless to humans, but some of them, such as the aforementioned Boomslang, are incredibly dangerous.