A good way, maybe the best, would be to get to know a Slovene, or even better, a citizen Ljublaja. Slovene people, I would dare to say, are relatively friendly and it is quite likely that before you would say goodbye you would be invited to come and visit. Besides a bed you will also get a local guide, which is priceless.
If you don’t know a Slovene yet, than you should learn how to tango. Well, this might sound a bit strange way to find a place to stay at first. but tango scene is very strong for a country so far from Argentina. There are several tango groups in Ljubljana, they all proudly nest a few excellent milongueros. So, if you can tango, just find a milonga, have fun and you will end up knowing great people who might find you a place to stay.
If all this sounds too uncertain for your life-style, try CouchSurfing. After registering for free, you will get a chance to browse between couches that citizens of Ljubljana, from the world-wide community of CouchSurfers, offer for people like you. Don’t worry — CouchSurfing works, there are ways how to verify the couch-owners.
If this is to hippie for you, than you get to AirBnB. This is real people letting or subletting their homes for certain periods of time. You can get very good price/space deals. Like 40$ for a 70m² apartement.
If you dislike personal touch, than maybe you should go for non-personal style of a jail. Refurbished into a hip hostel called Celica. Celica is at the top of the Lonely Planet list as the Hippest Hostel and named One of the 25 Ultimate Places to Stay by Rough Guides. You will sleep in a former cell with bars on the door and on the window Hostel Celica on Metelkova Street in the centre of Ljubljana provides this unique experience. The former prison has been demilitarised only after Slovenia’s independence and the departure of the Federal Yugoslav Army. The renovation process was supervised by more than 80 Slovenian and foreign artists who are proud members of the Sestava Society.
You will find a good deal in hotel Park, a calm place with a running track as a neighbour situated at Park Tabor, wich is walking distance from city center.
There are plenty of other small hostels and hotels that offer good deals. Good luck and enjoy!