You cannot cross directly into Famagusta from the government-controlled areas of Cyprus. Instead, you must cross the Green Line into the Turkish-occupied territory (known as the de-facto Turkish Republic of Northern Cyprus). The nearest place to do this is from the Strovilia crossing near Agios Nikolaos, which is located inside the British sovereign military base area.
In general, you will need to travel by car. Famagusta has no functional public transportation, and there are no regularly scheduled public transportation links across the Green Line (although private tour operators do operate across the Green Line during peak tourist periods).
Self-drive is the most common way of visiting Famagusta, whether in your own vehicle or a rental car. Bicycle rentals are not available. It's possible to travel on foot, but sidewalks are in very poor condition where they exist. If on foot, be very careful not to accidentally cross into areas quarantined by the Turkish army and/or the UN, as doing so risks arrest. Taxis are a better (and safer) option for the independent traveler without a car. These are widely available and generally inexpensive for either point-to-point trips or local tours.
Famagusta largely maintains the look of a war zone, with a bombed out and fenced off downtown. The fact that the city is largely inaccessible limits sightseeing opportunities. Enjoy sunning yourself on the public beach next to the ruins of once-posh hotels, surrounded by concertina wire. While there are no lifeguards, Turkish soldiers with M-16s provide plenty of security.
Gambling and prostitution are both legal, and are the primary forms of entertainment in Famagusta. There are numerous casinos, bordellos, and similar places of ill repute. Illegal drugs are also plentiful in Famagusta, with access to the Mediterranean Sea creating a popular smuggling route.
Fuel is available in Famagusta, and supplies can be purchased from a few small markets. Note the available supplies are slanted toward agriculture, which is the primary economic driver in the region.
Most of the larger casinos have restaurants, and they are probably your best bet. Otherwise, there are kebab parlors scattered around the city.
Food in Northern Cyprus is not prepared to the same standards of cleanliness or hygiene as in the south. The safety of tap water is spotty at best. Accordingly, the traveler is recommended to take appropriate precautions in avoiding food-borne illness.
The casinos will gladly serve you free drinks as long as you're gambling. Most of the brothels have bars as well. Otherwise, liquor, beer and wine is available from most corner stores.