Here are some examples in the Editor.
First, I want to dispel the myth that you can only transition from dirt to grass with grassy dirt, et cetera. It's totally not true. It looks good, but you need to do more than that to make it look natural.
In order to create this example, I made some big blobs of primary tiles (grass, desert, dark desert - usually upper-layer tiles which can cover a lot of area without looking bad) on top of the base tile (dirt). Then, I used secondary tiles to make some landscape features (rock, pebble, rough dirt). Then, I used our favorite, often-abused filler tile (grassy dirt) to fill in some areas around the grass near the road, under the impression that the grass would have been trampled somewhat but not enough to turn it into dirt or rough dirt.
Here's the tricky, time-consuming, and most rewarding part. Use your discretion to pick out harsh transitions or ugly corners. Anything that reminds the viewer of the World Editor tile grid. Then, cycle through the individual variations of both tiles. You'll usually find 2-3 variations which transition between your tile and each other primary tile in the tileset. Make sure to uncheck "Place Random Variation" above the texture display panel, and use these transition tiles to add diversity and create a natural aesthetic.
Once you get the hang of which tiles work with which within the default tilesets, you can start shifting tile order around and adding tiles from other tilesets and get creative with stuff that's "not supposed to happen." But I wouldn't recommend it until you know how to work a default. Transition tiles and the edges between tile types provide excellent opportunities for doodad placement. For instance, you can use a transition between rock and dirt to blend a rock doodad into a hillside or flat dirt area. You can use a transition between dirt and grass to outline a shrub, or a transition between dirt and rough dirt to highlight where a tree is bursting from the ground. You can strategically place a rock doodad along the transition between grass and rock on an incline to make the top of a rock face look sharp (or be lazy and use it to cover up an ugly grass, dirt transition).
Play around with it and you'll see what I mean. Enjoy!