Bansko, the popular ski resort, is an important entry gate for the Pirin range.
Another popular entry point is via Sandanski, about which this article is lacking. Please update if you know information about this!
A cheap way to arrive to Bansko is by train, and coming from Plovdiv or Sofia you will have to transfer first at Septemvri station. From either city, the train should cost about 10 lv for the whole trip. It takes a couple of hours to get from either city to Septemvri, and from Septemvri expect about 5 more hours. From Septemvri, there are around four connection every day to Bankso, two in the morning and two in the afternoon. The views are beautiful and you can easily pass time just enjoying the breeze from the train car door and taking in the mountains. Check the schedule of trains before setting out.
In order to reach the Banderitsa or Vihren huts/chalets (base camp to hike in the area) from Bansko, at least in the non-ski season, you will either have to hire a taxi (~$15), go with a tour, or hitchhike.
The best option to reach Pirin from Bansko for independent traveler(s) on a budget is to hitchhike, which is particularly easy during the summer with a good amount of domestic tourists heading up to either of the camps. To do so, walk south (gently uphill) from the train or bus stations though town until you reach the entrance to the Pirin National Park, indicated by a small house for information about the park. From there, the only cars going will be into the park.
Once inside you will have to hike, the different huts and summits are connected by hiking trails. There are many different options for hikes, with indications on how many hours each hike will take at a moderate, comfortable pace. If you plan to spend a while hiking, check with the tourist office (during normal business hours) to get a map of the area and plan out your hike.
There is a broad network of flagged trails through the mountains. The Pirin tourist map (1:50,000, avalable at local shops) offers a good overview of the trails and huts/chalets to sleep in.
Popular with domestic tourists, you can hike Mount Vihren, the second highest peak in Bulgaria (2914m). Round trip from the Vihren hut takes 6 hours; it is a beautiful mountain which offers beautiful views.
There are also plenty more trails to be discovered. The area around Vihren peak is quite barren, so you may want to hike in lower elevations if you want to explore more of the incredible pine forests in the area.
Vihren hut does not offer meals, but in the area around Banderitsa (about 30 min walk below Vihren hut) there is a fair-priced and tasty roadside restaurant. For example, a good breakfast will cost around 4 lv, and a dinner with beer will be around 10-12 lv. A hearty salad will be 4-5 lv.
There is a network of mountain huts/chalets, which offer rooms and bungalows (bungalow for about 20 lv for two persons). Bring your sleeping bag just in case, but you can expect that a dorm room in the hut will provide clean linens and a blanket.
To sleep in the dorm in Vihren hut, 20-30 minutes up from Banderitsa by foot and 3 hours from the peak of Vihren, it will cost 12 lv pp.
Alternatively, there are marked camping areas around the huts. There is a popular, inexpensive tent camping area around Banderitsa close to the restaurant and water source, about 20-30 minutes walking slightly downhill from Vihren hut/chalet.
If you arrive too late to make it up to Banderitsa or Vihren huts from Bansko, there are places in Bansko to stay that offer fairly cheap rooms during the non-ski season. A place only about a minute walk north (toward town) from the park entrance called Apartment House Comfort offers single rooms with nice amenities (internet, no breakfast) for 20 lv, or 15 lv pp for a double. Surely, similar deals could be found in other hotels.
It would be great to have more information about coming from Sandanski, though. Update this if you learn anything!