Taxis are really easy to find and are easy to get around using them. of course it can be used to get to other emirates too. Look for the unmetered Ajman taxi- by offer cheaper prices than the offical metered ones e.g. 10 dirhams to Sharja, 40 dirhams to Dubaibest during the peak times.
Look at for shared taxis that wait for 4 people to come and take the taxi, where you pay 10 dirhams to dubai when 4 people are sharing the taxi. These are "unofficial" taxis, located in the Somali area of Ajman.
tour buses: guided tour buses can be found at top hotels where can arrange a tour to ajman and main attractions in it.save your work after visiting, otherwise everything will be recovered and given a chance to be eaten by thambaia