PU's can be quite useful for expansion anywhere, however, only PU'd countries that have the same culture group as your own will grant you cores when you inherit it. Still useful for a different culture country, but you'll be given a heap of provinces with 50 years to go till they core when you inherit.
you can inherit countries in 2 ways. 1) wait 50 years after starting theunion, have good relations, and there's a force annex option. It takes a lot longer though. Option 2) Have great (195+) relations with the country your in a union with, and on monarch death they'll probably be inherited into your nation. Every time i've had a monarch die and a union with 195+ relations its happened, not sure if its the required conditions or just a fluke.
Its also worth noting that if the country's relations is less than -100 when your monarch dies they leave the union.
Now, getting unions, that's a bit more tricky.
As far as i know, having a good diplomat as a king and having royal marriages with other countries, who's heirs don't have a great claim to the throne, will give you a chance to form a union, as outlined much better above. seems you need to claim the throne in this case too.
However, the easier way to get a union is to have a royal marriage with a country that has no heir, (and isn't in a regency council), and have more prestige than them, click the claim throne button, and then declare war on them to enforce a personal union. The only downside, of course, is that you get a -50 relationship bonus with all other countries you have a royal marriage with (including other nations you have a union with if your still on your first monarch with them), and lose 20 legitimacy.
Luckily the game gives you a handy hover over list up the top of a list of a list of nations with disputed succession (eg any nation without a heir). going into the message settings and changing it to pop up whenever a nation changes ruler can help you keep an eye on a nation you want to PU (aragon as castille, or vice versa, etc). The other main thing to remember is that you need to keep your prestige up, so a prestige giving advisor can be handy.
edit: bah, beaten
Claiming a throne costs two things: 50 legitimacy and -100 relations with every country you have a royal marriage with. Doing lots of RM's will make your next throne claim painful, but without very many it'll take forever to claim another throne. Decisions, decisions.
I'm pretty sure its only 20 and -50. As i said above, don't bother with a web of marriages, just form them whenever a throne is disputed. The ruler change popup helps immensely.
For example, in my recent Brandenburg game i got lucky and the king of Luxembourg died in the first few years (after i'd insulted down to -100 relations of course). I noticed Brunswik had disputed sucession, RM'd them, claimed the throne, then declared war on them, won, and PU'd them (and vassalised another nation that i needed for forming germany, to use a "incorporate" free core later). The country to their north that i needed also came up, so i did the same to them. I bribed both of their relations up to 195+, and when my king died i was up 3 cored territories!