The Giza Plateau itself is walkable once you are inside the gates, though the distances are larger than they look on a map: from the main entrance to Menkaure's pyramid at the far end is a 2 km walk across hot, sandy terrain. Horses and camels are available inside the complex — negotiate hard and settle the price before mounting. A camel circuit of the plateau takes about 45 minutes.
Within greater Giza, taxis and the Uber/Careem apps are the most practical options. Egyptian Uber drivers almost never speak English but the app handles navigation, so it works well. The main Cairo Metro Line 2 runs through northern Giza with stops at Giza and Cairo University; it is cheap, reliable, and avoids the traffic. Microbuses (shared minibuses with fixed routes) serve most local destinations for very little money if you can figure out the system — ask your guesthouse.
For excursions to Saqqara, Dahshur, or Abu Rawash, hire a taxi for the day. Drivers offering pyramid tours will also take you to these sites; negotiate a full-day price rather than per-site.