6 weeks in Peru seems an awful lot of time; and indeed it's a good timeframe to explore the main sites and attractions in Peru. Still, this vast country would deserve more than only this.
We stayed in Peru for a bit more than 6 weeks, starting out with a 2 week Spanish course in Cusco. Although the most touristic town in Peru, it is a fantastic place to stay for some time and explore both the city as well as as the surroundings with it's many archeological sites. Most of the sites are easily accesible with public transport, e.g. collectivos or buses. The fare system in Peru's public transportation is transparent, mostly the fares are displayed inside the busses and the 'cobradores', money collectors inside the busses, won't charge more than that.
The main site to be visited out of Cusco is Machu Picchu. Also this can be easily done without going through a travel agency. For information on where to catch which bus or collectivo, as well as on where to buy your ticket for Machu Picchu we highly recommend going to the tourist information office close to Plaza de Armas where they'll supply you with a good map and also inform about the fares to each site. Here you can also buy your Boleto Turistico, in case you plan to get this.
First step is to reach Aguas Calientes / Machu Picchu Pueblo. This can be done by train (Perurail or cheaper Incarail starting at 50 USD one way) out of Cusco or Ollantaytambo. Both have got their offices at Plaza de Armas in Cusco.
To reach Ollantaytambo take the bus or faster a collectivo (10 Soles).
Another way is to reach Hidroelectrica from Cusco or Ollantaytambo by collectivo or minivan. Out of Cusco many agencies will offer the full 2-day tour via Hidroelectrica at prices as low as 100 USD pP, but for a more relaxed approach you may as well book only the transport to Hidroelectrica (and possibly back). Just ask around in Cusco. From Hidroelectrica you can easily walk in 2,5-3 hours to Aguas Calientes, following the train tracks.
Once in Aguas Calientes, don't be shocked by the way it looks and by the prices there. Find your hostel, negotiate the roomprice down and for cheap food head to upper floor of the market (only during the day).
Before heading to Machu Picchu make sure you've purchased your entrance ticket to it; this can be done in Cusco or latest in Machu Picchu Pueblo! If you want to hike Wayapicchu, a 1-2 week lead time is recommended.
To get to Machu Picchu simply walk up at dawn or take one of the first busses starting at 5.30am (10 USD one way). In the early morning hours the place is still reasonably empty and you'll get the chance to enjoy some solitude before the first groups of day tours arrive from Cusco.
In the early afternoon you can walk back to town and catch a train to Ollantaytambo, where you can stay another night to explore the ruins there the next day. If heading back to Hidroelectrica, we recommend staying one more night at Aguas Calientes, as otherwise you'll have to leave Machu Picchu as ealy as around 11am, in order not to miss the last collectivo / minivan leaving Hidroelectrica at around 3 or 4 pm.