To make the basic blocks, you will need a 2x2 bit of dimensional lumber (typically eight feet long and about 3 bucks), a saw to chop 2x2s into inch-long segments, some stain to color your wood, and a method for sanding the corner bevels. You'll also need some glue, maybe a small brush, and a cup or tupperware of some sort. For the notable tools, I use:
That's a cheapass Ryobi miter saw ($60), some food coloring (the neon stuff was about $3, the big precision color kit... $20? Candy-making leftovers, there)... And a low-end Dremel rotary tool (which is sitting on the dremel workstation - that's not required for the basic stuff).
Now, there's a good chance you could do the cutting with a vast array of other saws just as well, even a hand saw and cut box if you have the energy, but... Whew.
I don't think you can really beat food coloring on price. That's just a winner.
You could likely sand the corners a number of other ways, as well, but a Dremel is not so much "A tool to find a replacement for" as it is "A tool that can replace half the other fiddly little crap in small woodworking".
Step One is "Chop up the 2x2 into inch-long segments". You could go longer or shorter - as you like. The size of the chop is the height of "ground level" off your table.
To me, a variance of 5/8th from one "level" to another on hills and the like is favorite, and a full inch means I can later add blocks that are below basic ground level. Also, I wanted the blocks to have enough weight that I wouldn't need sticky pads on the bottom, and so on.
Step Two is staining. I just use a tiny little tupperware tub, fill it up (it's about an ounce), add food coloring (typically a total of 5-9 drop per ounce of water), and then brush it on or just dunk the pieces one side at a time like so:
After staining, stand the pieces up on some scrap wood, paper towel, or other surface, and let dry (I leave them overnight).
Step Three is taking each block and sanding a bevel around the top edge. This gives a nice white line once you sand down under the coloring.
The hill top center there is five piece at 1 inch and 5/8ths, and four more pieces at 2 inches and a quarter long, respectively.
When gluing, do it with some kind of supporting angle. I have two piece of baseboard screwed on top of my work bench in a right angle. I put the first piece in that corner, and then glue the others to it, pressing the whole module against that into "square-ness" as I add pieces. This method is pretty crude, but it works well enough for this; you might want to use long clamps or some more professional method to get it working as you want.
A quick note here: If you actually want to reproduce my scenery as-is, you just need the neon colours (which give a nice pastel when used sparingly) for the basic blocks. The secret sauce is:
Grassland: Ground at one inch, hills as above. Color is seven drops yellow-green, one blue per oz.
Water: Cut at 5/8th tall. Color is five drops of blue per oz of water.
Pathways: Cut as grassland; color is seven drops of yell-green, one drop blue, four drops red per oz.