You can use whatever software you would like that can read or write to the serial port. The "simplest" test would be to use something like putty or teraterm or hyperterminal, and type commands by hand. The E3648A uses a human-readable command protocol called SCPI.
The commands to use are documented in the user's guide of the power supply, and are things like "VOLT 0.5" or "MEASURE:CURRENT?".
The instruments are generally designed to be used through GPIB which has special interface commands to read status bytes, or send triggers, but the RS232 interface should be able to do nearly everything the GPIB interface can.
The baud rate can be set between 300 and 9600 baud (9600 8N2 should be the default) through the front-panel. (Note this is 2 stop bits, not the normal 1).
You can send a CTRL-C to the instrument to clear the RS232 interface.
You can then use your language of choice to communicate with the instrument (C#, python, etc). You can either use a native windows serial port library, or you could setup your intrument through "VISA". If you use VISA, then it would be easier to transition to GPIB control in the future, but wouldn't really give you an advantage at the moment with only a single instrument.
There is one more warning:
Do not use the RS-232 interface if you have configured the power supply to
output relay control signals. Internal components on the RS-232 circuitry may
be damaged.
Looking at its website, Docklight probably would work, but I've never used it myself.