As BrianR says, yes, you can go one-way, either way. However, since the same train goes back and forth on the rails, it travels in each direction only every other day - and then rests on the 7th. ;-) That means you have to synch your travel plans around the day the train is running in the direction you need to go. That was a little tricky for us but not insurmountable and "vale la pena" (worth the trouble). The ride ends in Puno so you will definitely have a chance to see Lake Titicaca. In fact, given the hour you arrive there (5:30-6:30), it makes sense to sleep over in Puno and then visit the lake the next day. The floating islands are so unique that taking even a half-day tour the next day would be well worthwhile and still leave time for you to get to some other destination the same day. (We hired a driver to bring us to Puno from Arequipa.) If you plan to fly to your next destination, the train stops in grim little Juliaca about an hour before reaching Puno. If your schedule is tight and all you would be able to do at Titicaca is look at the water but not tour it, you might consider leaving the train in Juliaca and going straight to the airport (providing there is a flight then). Otherwise, if you are flying, you will have to come back. I don't know if children are in your mix, but I have a slightly different take on taking the train with them than Brian's. Your ground transport options between Cusco and Puno/Titicaca are all longish. The bus or a car might beat the train by an hour, but neither allows the mobility that the train does or offers the entertainment. The open observation caboose was a constant source of delight for all of us and would be for kids; delicious snacks are served intermittently (food is always a great diversion); the meals are memorable; and there is live entertainment (indigenous music and dance) a couple times a day. There was a little girl (7 or 8) on the train with us, and she seemed enchanted. (The adults were, too.)

You’re travel agent should be able to sort that, we did a one way with our journey.

We are planning to travel by train on 15 December from Cusco to Puno and stay one night in Puno. what time the train leave and what time we reach Puno. I book the accommodation at Sonesta Posadas del Inca Lake Titicaca. According to train time table train leaving on 15th December.

We noticed the train only goes from Cusco every other day so we had to move some things on our itinerary. Also it is a full day trip - our 10 hour journey turned into over 11 due to some unforeseen circumstances.

This is a train company. I do not believe they will arrange travel from your hotel to the train station. I recommend working with your hotel on a transfer.