If you decide not to hike the Inca Trail or do one of the other treks and you want to go to MP by train you can buy train tickets online (Inca Rail or Peru Rail) from Ollantaytambo to Aguas Calientes. You can buy tickets for the bus from Aguas Calientes to the MP entrance when you are in AC.
We did a one day hike on our own:
We took a tourist shuttle from Ollantaytambo to Santa Teresa. We stayed overnight in Santa Teresa (and went to the hot springs). We asked around about transport to Lucmabamba early the next morning. Our hotel (Hostal El Sol) was very helpful and made sure a public van picked us up at 5 am. They dropped us off right at the start of the trail. It took us 2.5 hours to Llactapata (700 m elevation gain) and 2 hours to get down to Hidroelectrica. The trail is straightforward and once you reach the river you can ask as well (not that we really needed to). The only time we were a bit confused was at Llactapata when we tried to find the trail down. Facing MP the trail is on your left. It took us 2.5 hours from Hidroelectrica to Aguas Calientes (12 km). That is the part where you walk along the railway tracks. The Llactapata ruins are not that spectacular (although the part that is overgrown and crumbling has a certain kind of charm) but the view of Machu Picchu from there is amazing! Be patient though as we had to wait for the clouds to lift. Also, the walk up and down through the cloud forest is great (flowers, birds, butterflies, views).
Most people on our shuttle were taking the shuttle all the way to Hydroelectrica and then walked to Aguas Calientes from there. So if you don't want to do the hike via Llactapata just stay on the shuttle all the way to Hidroelectrica.