I am starting a new game and would like new tilesets. I have found some I like, but don't know how to download them so I can use them. Any help?

Just download the image and put it in the location Graphics/Tilesets in your game directory.

I wouldn't recommend putting it directly into the folders Directory, use the import feature so you can set the transparent and semi-transparent colours. Wasn't sure if that's what you meant there when you say 'put it in'. Just to expand on the importing:

Use the MaterialBase Icon (Looks like a folder with three sheets of paper).
Goto Graphics/Tilesets and click on Import...
Find and select the tilesets you've saved.
Left click on the background colour and use the right click for the shadow colour.
Click Close

Then go to the Database icon and the Tilesets tab.
Change Maximum at the bottom (Increase the number to however many you like)
Click on one of the new blank ones at the bottom and give it a name.
Use the > Icon under Tileset Graphic and select your new tileset image that you imported.
After that then it's a case of setting the options at the right hand side. This basically tells RM what parts you can and can't walk on and the priority which is basically for trees and things you can walk behind even though you're visually on the same tile.

No it wasn't. It's just that I almost every time use GIMP or Photoshop to make the images transparent, therefore, I don't use the Materials too often.

The internet is your friend. If you are fucking lazy like me, just save it into the tilesets folder. I'm a VX user, so i'm not so smart about XP, but it should be the same. If you have effort, just import it via the Resource Manager or whatever it is called in XP.