Wort stuff. Partal Mash? AG?

I want to make a batch of beer this year. I haven't made a batch from scratch for at least 7 years. I remember one step I took was to pour hot water on the grain and let it sit in a cooler for sometime. After that, I flushed the grain with fresh water into my kettle and added the wart juice. I don't want to buy another cooler for what I think is called making the mash. Can I just heat water in the kettle, add the grain, and mash with it under a heat source at a consistent temp? Then add my water to the kettle and start to brew? I have almost all the tools available, I want to avoid buying a cooler. Maybe I could use a styrofoam cooler if I have to do this process.
Advice?

Paul

You're generally close, but there are some key missing items.

I'd suggest spending some time here and get up to speed on the basics.

Then you'll have enough info to proceed and we can offer up answers to more specific questions.

Cheers.