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It is complicated situation in the nullsec. Immediately after coming out of the gate you find yourself in the "Mobile" (Mobile Warp Disruptor) or "Bubble (set by Warp Inderdiction Probe). You can get away if you have a Cloacking Device aboard, or if you have a very fast ship with MWD (Mobile Warp Drive), or if the Bubble had been set hastily and crooked.
When the Bubble is not set properly, you should just warp away, ideally to a safe-spot, or station. Maybe it's not always possible, but the Bubble or Mobile Warp Disruptor should not impede you much.
If the Cloacking Device is aboard, you need to find a moment during after jump invisibility period when all fast enemy ships will be away from you. And then you need to quickly go to the edge of the “mobile», but not in a straight line "gate-Mobile Warp Disruptor edge", with activated MWD and AB (if any), and immediately activate the cloacking device. If done quickly — you'll glimpse in the review of the enemies, but they will not have time to lock you. If the enemy manages to lock you, or any object  is at a distance of 2 km from you, you won't be able to activate the cloacking device.
But even if you go under cloacking, Interdictors can still knock out your ship. Therefore, you should get out of the “mobile» under cloacking, accelerate to a selected object in the system (stations, gates, or a planet), and then warp.
If you have Mobile Warp Drive, you should go back to the gate (taking a pause of 20 seconds, but no more than 30 seconds — afterjump cloacking will end). During those 20 seconds, you just need to right click for the next gate, and select Set as first waypoint. Next you need to quickly turn on the autopilot which will lead the ship to the selected point and press the button MWD; after MWD is activated, attemp jumping through the gate. In most cases, jumping through the gate will occur even if the ships was damaged, either on autopilot, or manually.
Another important thing is to learn the size, appearance, and the names of all Interdictors. Thus, the Minmatar one is named Sabre (the most dangerous), the Amarr - Heretic, the Gallente - Eris, and Flycatcher at the Caldari.