The Tesla turbine was originally a steam powered turbine.  There have been attempts to run it with a compressor added in front.  It is apparently not efficient enough to run as a gas turbine.  Basically the turbine consists of a bunch of disks with a small gap in between.  The flow of steam or air or water drags the disks along to cause rotation. 

Tesla was such a gifted inventor that people assume and make all kinds of claims for his mysterious turbine.  There are also scams out there for working magnet motors of fabulous output that you can buy for the right price and some bridges also.  The Tesla turbine has found some success as a pump to pump abrasive slurry.  Other than that I know of no other successful use
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If you chose to build one you will need a steam boiler along with that water.

I believe Tesla's turbine was intended to operate like a gas turbine, He patented a mechanism refered to as a "valveular conduit" which has no moving parts but acts like a check valve ---- having one way flow. This valveular conduit would be combined with a gas burner on the input to his turbine producing a high output engine with one moving part.Tesla mentions water injection to cool the hot gases to prevent warping of the turbine disks. The machine itself would then act very similar to a valveless pulsejet engine only very much more efficient and having none of the issues of blade erosion found in present gas turbines. What everyone has completely overlooked is one simple fact--- the input was pulsed--- a slug of gas and air would ignite pressurizing the turbine input instantly which would destroy "normal" turbine blading but not teslas turbine, a pulse of water would then be injected at the input condensing the remaining gases rapidly and sucking in a new charge of gas and air through the valveular conduit. There is no turbine other than Teslas bladeless turbine which could handle these extremes of changing accelerations, none!

I know that these have been used "in reverse", driving the turbine with a motor or other mechanical input so that the machine acts as a pump.  One application is a high-powered "water cannon" used for excavation.