Sorry, I misspoke with the word "fabric". I meant to say "cloth".
Take a look at the Hypershade (Window -> Rendering Editors -> Hypershade). In the left pane, you'll see all the different types of render nodes you can create. Scroll down to 2D Textures, and you'll find Cloth is the third one down.
Here's how to get started using it:
1. First create a surface material by clicking one of the buttons under Surfaces, or choose an already existing material. I'd recommend starting with a Lambert, to keep things simple. You can experiment with other material types later.
If you want to work with an existing material, you'll find all that are currently in the scene listed in the upper right pane of the Hypershade, under the Materials tab. Right click on the one you want to use, and hit Graph Network, to open it up in the Work Area (lower right pane).
2. Now click the Cloth button. You'll see a cloth texture node appear in the Work Area, near the material node, along with a texture placement node.
Note, there's an options toggle under 2D Textures for creating new textures either normally, as a projection, or as a stencil. For now, lets just keep it on Normal. You can experiment further with projections and stencils later on.
3. The next step is the connect the cloth node and the material node together. Do this by middle-dragging the cloth node onto the material node. A pop-up menu will appear, asking which of the material node's input channels you want to use. For now, just pick color. Later on, you'll want to experiment with other channels. You'll find that cloth works quite well for things like bump, displacement, specularity, etc. But for now, keep it simple.
4. Apply the material to a piece of geometry. To do this, simply select the material, shift-click on a surface to add it to the selection, and then right-click on the material and hit Assign Material To Selection.
5. All that remains now is to adjust the cloth settings, and the texture placement settings to your liking. To adjust any node's attributes, simply double-click on it in the Hypershade, and it will open in the Attribute Editor.
Note, by default the Attribute Editor will open in the main Maya window, to the right of the viewer pane(s). While the Hypershade is a floating window by default, the Attribute Editor is not; it's docked. If you really want to, you can change that, but it's more trouble than it's worth. I wouldn't recommend it.
The attributes for the 2D texture placement node should look somewhat familiar to you. They're very similar to the repeat & offset settings on the Texture tab in the SL editor. The attributes for the cloth node are pretty self explanatory. Play around with all the settings to get a handle on what they do.
If your graphics card can handle it, work in high quality mode in the viewer pane (Renderer -> High Quality Rendering), so you can most easily see the effects of your changes. And of course, do test renders with Turtle often.
That should be enough to get you started. There's a ton to discover and learn, obviously. Keep playing.
