There are a number of steps to achieve this. Assuming the Arduino is in the robot, it would be programmed to receive ASCII characters (text strings) via the serial port. You would invent some sort of protocol, for example the Arduino sends a prompt when ready to receive commands, (i.e after receiving a command) and the commands are sent as one or more characters followed by a terminator (carriage return as "enter"). These can be whatever you decide. The Arduino receives this string, places it in a variable, and parses it to extract the meaning of the command. There could be a few rules in the protocol designed to reject false or garbled commands. These can be "it must be the expected characters, perhaps always proceeded by a preamble like a $ sign". The command from a keyboard could be automatically assembled into a packet with checksum and length for example, before it is transmitted. This allows a false command (due to noisy communications) to be detected if that is an issue.
This can be tested initially using a PC and a program called a terminal emulator, that just sends whatever you type out of the serial port as an ASCII character, and displays whatever is received. The connection at this stage is a serial RS232 connection, using a serial port from the PC and wires. If it has no serial port, use a USB to serial (RS232) converter. Also you could write your own software for the PC, which could assemble packets etc.
The communication connection has to be considered. If this is under water, (you sid the pool) radio can only be used by trailing an antenna on a float, with a cable connecting this to the underwater device. Radio does not work under water except in special (and impractical for you) cases. If it is a boat on the surface, you have an antenna as high as possible (on the mast).
What radio to use? There are all sorts of radio modules around, but you prefer one that sends ascii characters. In other words it has a serial port. One idea is to get a Bluetooth to RS232 dongle for each end. It simply connects to the RS232 line at each end. The computer end (a PC) could use a USB to Bluetooth dongle. Some laptops may already have a Bluetooth port. Here is an example of stand alone add-ons which work with any serial RS232 limk to replace the cable:
http://www.sena.com/products/industrial_bluetooth/
These may need some understanding of the serial port handshake wires too. The antenna is inside these dongles, so you might mount the whole thing (less the shell) on the mast. It needs to be in a waterproof case. You can buy what are called OEM modules, these have no case or serial connector. Search for such things.