Will you help me cure my plant?

I bought some houseplants two weeks ago, for the first time ever. I am not good with plants. Predictably, neither of them look very happy. One of them had a bit of fluffy white substance around its twigs when I bought it, which I thought was just dust. The stuff has spread now. There are small flecks of white on all leaves, and the substance is bunched up around the parts where leaves grow out of. The white flecks have spread to my curtains, and I’m in a bit of a panic.

You can probably tell from my non-scientific description: I know nothing about plants. Help, please!