I need to build wood wall non bearing in a basement and attach the bottom plate to a concrete floor. What is the easiest and most secure method to do so. Should I use pressure treated wood for the bottom plate?
Thanks.

Buy you a cheap ram set gun from Lowe's or homedepot, it's a gun that you have to place a charge in and a nail for concrete and hit the top of the tool with a hammer which drives the nail into the concrete, it is safer than it sounds lol. I think there like 20 for the cheaper ones. Plus loads and nails

Also, use an adhesive like Liquid Nails... etc to attach the wood, if the nails should lose cohesion the adhesive will make sure it doesn't slip.

If you want to use another type of fastener, most home improvement stores have a wide variety of them, they will require drilling a pilot hole and hammering in, or the old 'tried and true' lead fastener and lag bolt.

Ken

First, do not use PT wood indoors.
Second, Isolate any wood that comes in contact with the concrete floor with some kind of water impermeable gasket material such as 6 mil Poly or "sill gasket"
For actual attachment you can use what ever you find easiest. For a small job you might consider just using concrete nails but if your concrete is more than 6 months old it will be Very hard and you should use either a power faster such as a RamSet or Hilti or a Pre Drilled fastner such as TapCon, Striker or even a screw and shield.
Keep in mind that your fastner doesn't have to keep the wood from lifting but rather keep it from shifting. The ceiling will keep it from lifing.

I feel the need to comment on the (First, do not use PT wood indoors.) pressure treated
This is code to use pressure treated wood for contact with concrete or brick. Now you don't want to use pressure treated in places that kids can chew on it but this isn't the case, and also pressure treated isn't the same as a few years back, it is a silicone based treatment not a poison as before.