By taxi
Taxis are sometimes hard to find, especially in commercial areas. Taxis are supposed to switch drivers at 5:30pm however often they will appear to do so much earlier. After 4pm, expect half of all taxis to display a sign indicating they are not for hire. In congested areas, especially 1-way streets with no convenient exit, taxi drivers displaying the for hire sign ç©ºè½¦ï¼ will often wave you away when you try to flag them down or stop the car to ask where you are going and dismiss you if it's not to an area they wish to go to. Be aware and plan accordingly if you have to be somewhere on-time. Please also be aware that the lack of adequate taxis in congested areas (WuHan Plaza, for example, people in WuHan are much more aggressive when trying to get a taxi. Expect to race to any car that stops and to hold your ground at the door for example if you're waiting at the front door, someone will jump in the back. Rates are relatively cheap at ¥6 on the flag and with around ¥70 getting you between almost any two spots you are likely to want to travel between. It is possible to get higher taxi fares, but usually only because the taxi driver has deliberately taken you on a longer trip which is, thankfully, not a common occurrence.
Airport taxis are the exception. Foreigners in particular are likely to get ripped off by taxi drivers at the airport. They will demand prices starting at ¥150 to go anywhere in the city. For reference, going from the airport to the middle of Hanyang costs about ¥50 typically. It is advisable to insist on the metre before the taxi starts moving and if the driver refuses, step out, collect your luggage and go back to the taxi stand. Note that this is not a serious problem in the daytime when there is a supervisor at the taxi stand who is an airport employee, rather than a taxi driver himself.
One oddity of the taxi system is crossing the bridges. Because of the traffic problems and snarls at the bridges, the city has instituted a system in which half the taxis are not permitted to cross the bridge on half the days. Basically, if the day of the month is odd, odd-numbered taxis are allowed to use the Number One Bridge. If the day of the month is even, even-numbered taxis are allowed to use the Number One Bridge. This system may extend to the Number Two Bridge this is not yet confirmed but it does not extend to the Number Three Bridge. In most circumstances, however, it is not advisable to use the Number Three Bridge as it tends to increase the taxi fares dramatically although it is an interesting ride.
By ship
The Yangtze River can be crossed by ferry for a very reasonable fee of ¥1.5. The ferry runs frequently starting at 7AM and ending at 9PM. It offers by virtue of its unique location some nice views of the city, the Number One Yangtze River Bridge, Yellow Crane Tower, etc. during the day and an interesting nightscape view after dark.
By bus
Wuhan has a cheap usually 2rmb per journey, efficient, but horribly bewildering bus system in place. The service has vastly improved compared to the past. It is the cheapest way to get around the city. If you have a local to guide you, it can be used to get from place to place with impressive speed if not comfort or safety. Without a local to guide you, you should better have a very good map and a good grasp of Chinese.