You can get context-sensitive help for most of GIMP's features by pressing the F1 key at any time. This also works inside the menus.
GIMP uses layers to let you organize your image. Think of them as a stack of slides or filters, such that looking through them you see a composite of their contents.
You can perform many layer operations by right-clicking on the text label of a layer in the Layers dialog.
When you save an image to work on it again later, try using XCF, GIMP's native file format (use the file extension .xcf. This preserves the layers and every aspect of your work-in-progress. Once a project is completed, you can save it as JPEG, PNG, GIF, ...
Most plug-ins work on the current layer of the current image. In some cases, you will have to merge all layers (Image->Flatten Image) if you want the plug-in to work on the whole image.
If a layer's name in the Layers dialog is displayed in bold, this layer doesn't have an alpha-channel. You can add an alpha-channel using Layer->Transparency->Add Alpha Channel.
Not all effects can be applied to all kinds of images. This is indicated by a grayed-out menu-entry. You may need to change the image mode to RGB (Image->Mode->RGB), add an alpha-channel (Layer?Transparency?Add Alpha Channel) or flatten it (Image->Flatten Image).
You can adjust or move a selection by using Alt-drag. If this makes the window move, your window manager uses the Alt key already. Most window managers can be configured to ignore the Alt key or to use the Super key (or "Windows logo") instead.