The Inca Trail can host up to 500 people per day, and strict permits are required. The other trails have far fewer visitors and don’t currently require permits.
Then there’s always the train if trekking is not your thing! Choose the two day train option, the one day option is a very long day, and nowhere near as interesting as the two day options. Plus, you get to visit the ruins in the morning, rather than the afternoon- which is usually busier.
Also good to know, the Inca Trail is closed in February but Machu Picchu is definitely not. The permits can sell out 6 months in advance, particularly for the middle of the year, the northern hemisphere summer.
There are many different options for trekking, from a few hours, to over a week. Most options include your last night at a hotel / hostel in Aguas Calientes, close to Machu Picchu. That’s a touristy little town from where a shuttle can take you up to the ruins - best done as early as possible in the morning!
Aguas Calientes is also referred to as ‘Machu Picchu’ town sometimes.