There are some means of transportation to choose from, the cheapest being a “Round-the-Lake” bus, which actually doesn’t do a full loop, only going a bit further than half-way around the lake and will cost you 80NT$ (just over 2€) for a day pass. We didn’t visit by bus, but it looked like a pleasant way to visit most of the highlights around the lake without much hassle.
You can also choose to take a boat tour around the lake, but the best ways to experience the surroundings at your own pace would definitely be renting either a scooter or a bicycle.
We rented two cheap multi-gear bicycles at Papago Rental Shop, for only 100NT$ each (less than 3€), and they did the job just fine. If you’re not that into sweating profusely (especially on a super-hot Taiwanese Summer day), they also have electric bicycles to rent for a day, (300NT$), as well as scooters (400NT$) (i.e., 8.50€ and 11.50€).