Getting into Gaza is both difficult and unwise. In fact, as of around 2003, all would-be visitors were required to apply in advance for Israeli permission to enter the Strip. The application is usually submitted through your embassy in Israel and, in theory takes between 5-10 days. In practice, it can take months, and if you're not either a fully accredited journalist or an aid/human rights worker, you're unlikely to get permission to enter Gaza from Israel.
It is possible to enter Gaza from Egypt through the Rafah crossing. The crossing was reopened for traffic on June 1, 2010 though some restrictions still apply and only large groups on NGO sponsored trips will be admitted. Egyptian authorities control only their side of the crossing with Hamas police operating the other side. However, Palestinians except for men between 18 and 40 are permitted to cross into Egypt visa-free. Reports exist of Hamas police asking for bribes of up to $5,000 to allow people, including Palestinians, out of Gaza.
By ship
The port of Gaza is non-operational, and Gazan waters, seaports, and the coastline are patrolled by the Israeli Navy. If you attempt to reach the Gaza shoreline by boat, you will be stopped by Israeli naval vessels, and turned back. Only boats with prior permission are allowed in. All boats coming from Gaza are allowed to venture 6 nautical miles into the sea. Any vessel crossing this line is fired on.
By plane
Gaza has no functioning airport, as the former Yasser Arafat International Airport IATA: GZA has been shut down since 2000. The airport was badly damaged by multiple bombings - the most recent in 2009 - and is unlikely to reopen in the foreseeable future. The Israeli Air Force monitors Gazan airspace with radar, and regularily sends patrols of drone aircraft and fighter jets over Gaza. A surveillance balloon is also tethered at the Erez Crossing. For the time being, the closest airports is El Arish International Airport in Egypt, or Ben Gurion Airport in Tel Aviv.