We are 2 middle aged couples traveling to Croatia in June 2015. We want to drive through Ljubljana (Slovenia) from Zagreb. We are U.S. Citizens, and of course we have passports. Is this an easy process? We will be headed to Pula.
As said by Michael Hampton, no additional documents other than passports are necessary for you, so: Yes, unless you come with a truck etc. (content check), it´s as easy as it can get.
Take (one of) the correct lane(s) for normal, private cars (see the symbols above in the picture, all border points look similar); hand your passport through the window, get it back, and drive on.
Note that the queue of waiting cars can get a bit long, especially in summer.
[Unconfirmed if it's still valid: In theory, at least at some locations there is an exit check of one country and an entry check of the other, but in practice, one part will check the passport and on the other side some policeman will stand around and just look at the cars while they drive past him.]
Live 15 min from that border. There will be to lines. EU/EEA/CH and All other. If you have EU/EEA/CH passport you have to get in the EU/EEA/CH line. You will need to show your passport of EU ID card. You will not be questioned, only your document will be checked if it is genuine. If you dont have EU/EEA/CH passport take "All others" and you will have to stop only on Slovenian side. (Croatian border does not operate). At Slovenian booth there will be Croatian officer who will take your passport and check it if you overstayed (etc) and you will get Croatian exit stamp (all non-EU/EEA/CH citizens get one). Then you will have to give your passport to a Slovenian border officer. He will check your passport and might question you why are you coming, do you have enough funds (etc) like all normal immigration controls. It my also happen that the officer dont ask you anything. If you satisfy immigration requirements you will get Entry Stamp. As both countries are in the EU there will be no Customs Controls.