Based on NEC code, this is the current conduit fill table
Conduit Fill Table - Resources
for the 14-50 plug, you should be using qty 3-6 gauge cable, black, red, white and 1-10 gauge ground cable- green.
so min conduit size is 3/4 no matter which type of conduit you plan to use, rigid, pvc, or flex.
you need to support that conduit 12" from any connectors and about every 6'.
The cable is 6 gauge for the hots and neutral, and 10 gauge for the ground. You can either run all single strand gauge cables in conduit or get 6/3 THHN cable which has it all inside insulation. Its pretty much comparable in price depending on the length of run.
outside that, your panel needs to be able to support 40 additional amps continuous.
if your house only has 100amps coming in, which most houses are, there is very little room for you to add another 40amp load. This is the hardest part about the installation. Its not really the wire, breaker, conduit, or receptacle. Its understanding your electric usage and calculating your electric load as to not overload your panel and wiring. This is why electricians charge what they do. Anyone can pull wire and follow NEC code.
So if you dont fully understand what you are doing, spend the money and hire an electrician. Its not expensive, and it prevents your house from burning down. More importantly it prevents harm and injury to you and your loved ones. You do not want to electrocute yourself to save $500, thats just not smart.