Starting from Rimetea, Piatra Secuiului is one of the many trails one can hike in the scenic Trascau Valley. The top can be accessed using several routes. I'll describe the circular trail I like best.
Head east on a gravel road once you park the car in the village center. Look for the red triangle trail sign and follow this for now. At some point, once outside the inhabited area you'll turn right and head towards the Students' Grotto. This large portal with a high ceiling is definitely worth a visit. You'll have nice views from up here although you still haven't started the steeper hike towards the top.
Continue on your trail until it intersects the blue cross trail. Follow the latter. You will have to hike a steep, gravelly path. Once at the top you'll have very nice views across the Trascau Valley with its villages and farms.
If you have the energy, before starting your descent, follow our route and hike the other high point (Coltii Trascaului) where you'll also have good views of the area.
Follow the blue cross sign back down to Rimetea. The descent is also pretty steep, take your time, your legs could be a bit tired by now. You may find the way back down to be the best part of your hike, with the rugged cliffs on each side and the tiny village in a distance growing larger and larger as you head towards it.
There are several small restaurants in Rimetea where you can get a traditional meal. Don't forget to ask for the local dessert: "somodi kalacs", a delicious cinnamon filled cake.