Basement, that means concrete floors. here in Texas we do not have basements due to the shifting soils.
First, get some latex floor levelor to patch any cracks or holes or and divots that will show up when the carpet squares are installed.
Second, will the floor ever get wet, like a washer overflowing, hot water heater spillling, or whatever?
If so, make sure your mastic or glue is water proof. Mastic is the glue that you will spread down for the carpet to adhere to. PLEASE READ CAREFULLY THE INSTRUCTIONS ON THE BACK OF THE MASTIC PACKAGEING FOR PRECISE INSTRUCTIONS. FOLLOW THEM TO THE T. ESPECIALLY THE CURING TIME FOR THE MASTIC BEFORE APPLYING THE TILES AND THE TROWEL SIZE FOR THE SPREADING OF MASTIC.
You want the tiles to be symetrical on both sides. Get some information in print on how to find the center of the room and then to divide it into fourths. You will begin in the center and only one fourth at a time and work to the sides. This way if you have a pattern in the squares, you will show the same design on each wall sides.
Start laying out the squares and have fun. Let the squares cure out for a day or so after application so that they will not slip around.
Very easy project. you will need a tape measurer, a sharp box knife with extra blades, a straight edge, a pop a straight line tool, and knee pads. Learn how to cut those wall pieces. Its hard to say over the typeset, but you lay one tile over the tile next to the wall, then lay another tile from that tile to the wall space, cut the tile and whamo, you have a perfect fit.