First of all, you should make sure that no one in the house turns on any running water for anything until the drain has been unclogged. The floor drain in your basement is usually the last stop on the line for all of the water used in your house, and so any running water anywhere above will only cause more water to back up in the basement. Of course, if you cannot use any running water anywhere else in your house, it is even more imperative that you are able to unclog the floor drain quickly.
If you happen to have a snake on hand, this may be the best option to try first. However, it can be a bit difficult to get the snake to make the sharp turn typical of these types of drains not long after the pipe descends below the floor. That is not to say that it cannot be done, but you should be aware that you need to make sure the snake turns the corner before it will be useful to you at all.
If you do not have a snake of your own, you may still be able to take care of the blockage without calling in a professional plumber. But first you have to find it. Depending on the layout of your drainage system, this may be easier said than done. You can also make a pretty big mess if you open up various sections of pipe looking for the blockage, so be aware and make sure you have something in place to catch the runoff and debris that may come out of the pipes when you open them.
You may also run into trouble if the blockage is actually outside of your house in the larger sewer line that runs to the street. Unclogging a drain with this type of problem is generally a job for a professional and there is very little you will be able to do on your own.