Permits are not widely available and you will find that they can only be obtained indirectly. For example, a deal transporting a package or passengers to a system requiring a permit. As there is a hefty 'permit violation' fine for those entering a system without one, the person you are doing business with is obliged to provide you with a permit (make sure you ask anyway).
There are three systems in Frontier that require visitors to have permits in order to enter legally. Once you acquire a permit it is kept for life. They often come in useful, not just for general and trading purposes around those systems, but also for military missions, as neither the Federation nor the Imperial Navy issue permits and expect you to have one already.
Ross 128 Prison Permit
Required for entry into Ross 128 (0,0)
Ross 128 is a Federal prison colony and as a result there are strict regulations on who can enter. A system already brimming with criminals doesn't want anymore trouble on its hands and the Federal authorities like to keep Ross 128 'hidden away'. Relatives wishing to visit their condemned loved ones require a permit, as will you for any other purposes. A Ross 128 Prison Permit can be acquired from neighbouring systems (especially Sol), and is a useful possession for Federal navy pilots to have.
Required for entry into van Maanen's star (0,1)
The Guardians of the Free Spirit who inhabit the planet Major in this system do not take kindly to intruders, especially ones who bring illegal acts and items such as corruption, prostitution, arms, drugs, alcohol and luxuries. They are a secluded and unfriendly people, who want nothing to do with the outside galaxy. The Federal authorities have promised to protect their home system and enforce a permit requirement to gain entry. The Guardian's Permit isn't very sought after, as only black marketeers wishing to offload luxuries and arms have a desire to enter this system. Law-abiding traders will see little point in ever going near this system, for it is a desperate place. Those not-so-law-abiding might be interested in the system's thriving prostitution scene. Acquire for yourself a ticket to ride, and I assure you they will. Should you want to visit, Tau Ceti is close by and often has people with tasks for you to fulfil in exchange for cash and a permit.
Commune Visitor's Permit
Required for entry into YZ Canis Minoris (2,0)
The wealthy idealists who first colonised this system did so under strict obligations that it was run under a strict communist regime. This wealthy system still maintains that strict communist regime and a permit is required in order to enter. The nearby Sirius system often has people wishing to do business with this system and they are more than willing to give you a valuable Commune Visitor's Permit.