This is more of a Tel Aviv survival tip, though parts of it should apply to other parts of Israel as well. In any country, getting around is crucial. Given Israel's small size, it's not too hard or expensive to get around – certainly when compared with transportation in the United States. I've picked up some general knowledge about and have some suggestions for getting around in Tel Aviv and Israel, and I'll share them with you here.
Taxis: Personally, while definitely the fastest way to get from place to place, I despise taking cabs in Israel. As in most countries, the cab drivers in Tel Aviv are rude and always looking to scam you. If you know your way around, you're generally fine since you can call the cab driver on it if he tries to take you for a ride. Otherwise, you're more or less at his mercy – pretend like you know where you're going. You can either agree to "moneh" (meter) or you can request a fixed price. I think the latter is illegal, but almost every cab driver loves to do it. Generally you can get 5 shekels knocked off the price if you bargain and know how much the ride should cost. If you live somewhere where there aren't cabs driving around, you can call any cab company and they'll have a cab at your door quickly. I have had good luck with "Kastel." Note: cab drivers are allowed to and do tack on extra money for additional passengers, travelling late at night, and for luggage. Another note: inter-city travel is not charged with the meter – there is a fixed rate between every two cities in Israel.
Trains: I've only taken the train once and it was a very pleasant experience. While not cheap, nor particularly frequent, if the train goes where you need to go, it's easy and fast. In particular for destinations like Haifa and Be'er Sheva, it's a good way to go. Their website provides useful information.
Subway: The Tel Aviv subway does not exist, but supposedly there are plans to build one, mostly with routes to the neighboring suburbs. The intended completion date is 2012, but whenever I discuss the subject with anyone, I just get a hearty chuckle and some rolled eyes.
Inner-city buses: Tel Aviv's buses are actually excellent – fairly cheap and reliable. Depending on the route, the bus can take forever, stopping everywhere, or it can be an express, reaching your destination relatively quickly. Most buses start and end at a bus terminal – Reading, Carmelit, Arlozorov, or the central station. My biggest gripe is that if you need to take two buses, you have to pay two fares – most cities (San Francisco, NYC, Chicago, Amsterdam) in the world offer free or cheap transfers. Because of this, if you need to take two buses and have a travel companion, you're sometimes better off taking a cab. There are, however, some ways to save money if you ride the bus often. One is a "kartisiya" – a prepaid pass of ten rides. The price comes to about a shekel less per ride. When you get on the bus, just ask for a "kartisiya". From then on, just hand the driver the pass, and he'll punch a hole in one of the rides. Another option if you ride more than twice a day, every day, is a "hofshee hodshee" – a monthly pass. These cost about 200 shekels for the one-zone pass and offer you a great deal of freedom. These are also available for purchase from the bus driver. Personally, I like unlimited passes in any city, but in Tel Aviv especially – it's a great way to get to know the bus system and the city itself, as you can just hop on any bus without thinking about the money. The biggest problem with buses in Israel, however, is that they stop at midnight (or earlier), and do not run on Saturdays or holidays.
Inter-city buses: I've taken several of these. They are almost always on time, reliable, and comfortable coaches. The beautiful thing is that you can get almost anywhere in Israel on a bus. In Tel Aviv, long distance buses leave from Arlozorov or the "new" central station (it's not so new, it's just newer than the old one). Some buses, like Tel Aviv to Kfar Saba leave from the Carmelit depot.
Shared taxis ("monit sherut"): This is by far my favorite means of transportation. Cheaper than a single ride on a bus, shared taxis ply popular routes much more frequently than buses, with fewer people, fewer stops, and a more direct route. They also run later than any bus and travel on Shabbat and holidays. They are large, typically yellow, vans with a taxi sign on top. You can hail it just like a cab from any bus station on the route it travels. If it doesn't stop, it's full. When you get on, ask the driver how much it costs to your destination as you are boarding – some times they'll try to overcharge you by a shekel if you don't know the price, but usually not. Within the city it's 5 shekels. You can pay once you are seated – just pass the money to the person in front of you. The only problem with shared taxis is that there aren't many routes – if there are none going where you need to go, you're out of luck. However, they're so good that I often walk 20 minutes just to take one – the advantages make up for it. It's also a good means of getting between cities (Natanya and Tel Aviv, for instance).
In general, getting around Israel is easy once you know your options. The Dan and Egged websites are good resources, as are their telephone support options. If you have any questions, maybe I can help – just post a comment.
Have a nice trip.