This short tutorial will help you design a pattern that tiles well—meaning that it can be repeated over a mesh without showing lines. Using a very simple mesh in Blender, you can see your design in real-time and correct any mistakes before you spend a lot of time fine-tuning.
Set up the Blender Scene
Open up Blender, delete the default cube, and create a plane (Create > Plane in the 3D View window toolshelf). You may wish to extrude more faces from it, but this is not necessary. In the 3D View window properties panel (shortucut: n), under Shading, check the box Textured Solid.
Open the UV/Image editor window. Switch to edit mode on the plane, select all vertices, and go to Mesh > UV Unwrap > Unwrap (shortcut: u). In the UV/Image editor window, click the New button to create a new texture. Follow the guidelines at Texture Guidelines#Technical Restrictions to decide the resolution of the image. Ensure that the Alpha checkbox is selected, and make sure alpha (A) is at 0.0 by clicking on the color sample box. Click OK to create the image.
Select all vertices in the UV/Image editor window and scale (shortcut: s) the UVs to approximately four times the area of the image. Position the UVs so that the image is the center of the UVs. If your texture will only tile on one axis, you may wish to shrink the plane on one axis and UV unwrap it again so that the image does not tile vertically.
Painting the Texture Pattern
Now, switch to Paint mode in the UV/Image editor window. You can now begin painting a very basic outline of your pattern on the texture in the UV/Image editor window, and see it appear on the mesh in real-time, as in the screenshot below:
The axes on which your texture will need to tile properly depends on its application. If you are, for example, creating a generic wood texture for texturing a wall, your texture should tile on both U and V axes (all lines and colors should meet up smoothly on opposite sides of the texture). If you are creating a transparent grass texture, it would only make sense to make it tileable on the U axis (left and right sides tile smoothly).
Paint slowly and carefully, and watch the 3D View window rather than the UV/Image editor window. If you are careful, you can make sure your lines match up when tiled. When you think you have the rough shapes of your texture done, you can export your image by going to Image > Save As Image in the UV/Image editor window. You can now import the outline as a layer in a painting application like Krita (Layer > Import/Export > Import Layer...) and use it as a template to draw your details and colors in a separate layer. When you're done, you can discard the template and the Blender scene.