You can dig it out by going deeply enough to find the common lateral rhizomes that send up new plants. I removed common milkweed, Asclepias syrica, because I found it too aggressive in my garden. After digging out the obvious plants, I've pulled baby plants while weeding as they appear. Since I didn't go after the rhizomes, I expect this will take up to 3 years. If you decide on herbicides, make sure you don't have monarch caterpillars on the plants and remove the flowers so pollinators don't land on treated plants.
Glyphosate is the most common herbicide used to eradicate milkweed. Application after the plant has budded and before it has bloomed is most effective.
In my own garden I just pull up the unwanted plants leaving just enough for the Bees and Butterflies.