<p>I'm trying to create a very simple form in an Access database. Whenever I drag a textbox on the form, a label gets created with it. I want to be able to move the label without moving the textbox,but whenever I try to do that, the textbox moves with it. Its like they're linked with each other.
Is there a way to separate them from each other so that they can be moved separately?</p>

Yes, but you are better off looking for the small square black box that appears on the top left corner of each control when you click the textbox or label. This box will allow you to drag each control independently. Don't forget Format->Align (Left,Right,Top,Bottom) it is probably more useful for tidying up controls than anything else.
You can separate the label from its parent control by deleting the label, clicking the detail section to ensure that no controls are selected, and pasting, but I would advise against it. You can do a number of useful things with labels that are related to controls and one of them is move the two together - this is useful when you have the form tidied. Another is to find the parent of the control, which is useful when using VBA to change controls.