As a layman, the best tool you have at home which might be helpful for determining an art forgery is a camera: you can take a picture of the art and send it to someone who knows about the painting or the artist. The accuracy of the answer will only be as good as your expert is knowledgeable. Aside from a camera, there is no combination of typical household goods which will help a layman determine the authenticity of a painting in the general case.

If you know something specific about the artist, like that they only painted on canvases larger than a certain size, then you could use a specific tool, like a tape measure, to see if the painting is an obvious fake. But there is no way, in the general case, that a layman can do this. In fact, this task can be difficult for an expert with the best forensic tools. There may not be any way to prove a painting is an original, even if there are many ways to prove a painting is fake.

Putting a painting in your mouth won't help you determine whether it's a fake or not - thought it might help you determine whether or not it is a cookie. Among art lovers, such a move would be considered to be in remarkably poor taste. But seriously, don't put paintings in your mouth - some paints are toxic.
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