I'm guessing that by mountains, you mean uplifted areas not formed by volcanism. The term 'mountain' can actually be used to refer to any uplifted area regardless of process, but we'll use it here to talk about elevated areas that are formed in some way other than volcanism. There are a few ways I would determine if something was a mountain or a volcano.

First, volcanoes tend to have a conical form and can be isolated on the landscape.

Mountains, however, are formed by regional stresses that act over the entire landscape, so they tend to occur in broad chains .

Try this:
set a piece of paper on the table and push the ends together. You don't get a little bump in the middle of the piece of paper, but instead, the whole paper folds, right? This is like forming mountains, the rocks in a large area are folded and faulted. You can also look at rock types and structures to tell the difference. Surrounding a volcano there will be layers of lava that may be relatively undeformed (meaning that there hasn't been too much folding and faulting). You should also find ash and other debris ejected from the volcano when it erupted. In mountains not built by volcanism, the rocks will be extensively folded and faulted, and these folds and faults can be traced out over long distances. But beware! Many times, volcanism occurs during mountain building, so things can get very complicated.