I live in a three level house (basement, main and upper floor) my air conditioner (located in the basement) works but does not cool the upper floor as well as I would like. How can I get more cool air to the upper floor?

Not very easily. It is such a common problem. It is also something that could be completely solved when the house was built.

Now, it is more difficult to deal with. Sometimes the system can be zoned, warning, it really must be done right and is expensive. Or another option is install another A/C system just for the upstairs, even more expensive.

The usual advise is to close most or all of the basement and first floor registers to force more air upstairs, warning, this may not be a good idea. An A/C unit needs a lot of airflow to work properly and builders don't install extra registers and over sized ductwork. Doing so will actually lower the cooling capacity of the unit, slug and damage the compressor and possibly freeze up the evaporator coil. You can close a few and a few more about 50% but that is all you should try without knowing the static pressure and CFM of the AC unit.

Would an increase in fan speed help?

It can help, but the trade off is less dehumidifacation, that is very important in the way the air feels. It can even blow a mist of water, off the evaporator coil and into the insulation and ductwork, promoting mold growth.

Does the blower fan have only one speed?

Most likely yes, but is probably already on high, if so you need more HP