Hi,
Not even sure I'm in the correct forum but,
I want to attach vinyl lattice to vinyl siding so that I can plant trailing rose bushes along the side of the garage.
How do I go about this?

It is probably too late to say so now, but I wouldn't.

There is nothing structural about vinyl siding that would make it capable of holding the weight without deforming, and since it moves according to temperature, you could impinge on how it does so and cause other probhlems down the road, or if you use screws or nails, you would be providing a hole for water to penetrate the siding which is intended to keep water out.

What you should do is to get a couple stakes to fasten the lattice to separately

Excellence is its own reward!