Hitchhiking is very common in Israel. Hitchhiking is often done by pointing to the ground with the hand far from the body, instead of raising a thumb. But possibly raising a thumb will be understood as well.
The most usual way to start an hitchhiking journey is to take a bus out of town, to a junction in your direction. Almost every junction has a hitchhiking spot (the famous Trempiyada), or at least a bus station where drivers can stop. It is very hard to hitchhike from the cities themselves, and inter-urban buses are relatively cheap and can get you to the nearest junction.
Like always, precaution is needed when hitchhiking, although in Israel hitchhiking is a way of life. You will find hitchhikers everywhere. Your best bet for getting a safe ride in Israel is getting into a car with people who know what they are doing. Even still, caution is necessary.
You should remember that as a country in a sub-tropical region, it can get very hot in Israel, sometimes as early as March and as late as September. If you can, before hitchhiking check the predicted weather in the region of your travel, and if it's going to be hot, don't ignore it. Exposing yourself to Israeli heat without caution can be dangerous. In hot days, wear a hat and drink a lot of fluids. Suncream and sunglasses are also recommended.
Cities and locations
Note: Israel shares borders with these countries; however, due to hostile relations between the states, it is illegal and probably impossible to cross over to Syria or Lebanon; Getting into Palestinian territory in the West Bank is quite straight forward, usually flashing your passport in the checkpoint is enough. Getting to Gaza should be problematic. Egypt and Jordan should be fine.
Israel currently run 3 border terminals with Jordan:
1. In northern Israel, next to Beit Sheaan, you can cross in the Abdallah bridge crossing, from which it is quite straight forward if you continue onwards to Amman.
2. In Palestine (the occupied territories) the Israeli forces run the Allenby bridge crossing, seperating Jordan from the Palestinian territories. Because of its location, this border is only crossable to Palestinians and internationals (not Israelis) and the passengers are subject to intimdating "security" interrogations. This is also the most direct border crossing from Amman to Jerusalem.