There are a series of different ways of doing it. All rather complex. yes minority parties get a chance of representation. Depending on the type of PR you get a threshold below which you get no representation. You can retain a link to constituencies if you want to – this tends to mean less proportionality tho.
In scotland we have two systems. For Holyrood its an additional member system. You get two votes – one for constituency which elects around half the MSPs and the other for a list which is used to top up the parties representation so if they get 40% of the list votes but only 20% of the constituency seats then the list is used to top up. The lists are also regional. This means its a fairly high threshold to get representation – but still a couple of greens and a couple of others got in.
For the council we have multi member constituencies. Each constituency elects 3 or 4 representatives This gives a proportional element but a very high threshold. Edinburgh city council has a green or two on it tho.
Neither system is perfect and there are other systems around. I am a bit of an political geek and I am not 100% sure I have this explanation right. There has also been some fiddling with the scottish systems – previous holyrood elections used a slightly different system which had a lower threshold to get representation – so there were more greens and SSP and so on.
Beyond this you get into serious election geekery
http://en.wikipedia.org/wiki/Proportional_representation