One of the best things about being frugal during grad school is that no one has high expectations for your living quarters. Secondhand furniture and DIY projects are socially acceptable ways to furnish your home, which you can do at much lower cost than you can with new furniture.
You can find free or low-cost furniture for sale on locally-focused websites like craiglist and freecycle and a thrift stores.
If you can time when you obtain your furniture, the start and end of the school year at or near a university can be a great time for deals on furniture from other students who are moving or leaving the area. This is also a perfect time of year to rescue furniture from the trash (“dumpster diving”). Dorms and large apartment/townhouse complexes that are popular with students will often have furniture and other high-value items abandoned near the recycling area, which is a common signal that the item is free for the taking on a first-come first-served basis.