So you want to play a police officer, and not because you just think they're cool, but because you're really looking forward to using your skills and intellect to deal with crazy and uncertain situations. Perhaps you want to be a detective so you can deal with higher level cases, or a forensic scientist so you can conduct autopsies, and you figure that roleplaying it is the best chance you're going to get to really experience that 'Aha!' moment when you solve the crime.
The only thing is that when you rock up to game you notice a disturbing trend. Your case-solving skills basically boil down to rolling appropriate skills and hoping the Storyteller throws you a clue. You don't take any notes which means that you also have to keep rolling your system's equivalent of an Idea or a Know Roll to remember that little, yet pivotal, clue dropped awhile back. In other words, it's frustrating because you want to play a character that, in truth, you don't know how to play and there's only so far a good Storyteller can take you.
So what do you do?
Head to your nearest library and pick up books like Writer's Guide to Police Procedure (writer's guides are great for breaking it down into easily understood details), Idiot's Guide to Forensics, and general informative guides on any areas relevant to you. You could also always purchase them first-hand or scour second-hand bookstores for them as well if you want to be able to keep it handy. For Forensics, by the way, may I suggest Forensics: A Guide For Writers by D.P. Lyle, M.D. in the Howdunit series. You'll know more than you need to know at the end of it!
Depending on your relationship with your Storyteller and their personal style, you can also loan the books to them so that their clues can actually match the facts. But heck, even if they're not going to know the precise details of what happens to a crispy human, you can just pretend its Television Science and use all of the tricks of the investigative trade that you've read about it. Even if you have to rely on the rolls to understand the facts, you'll still know that you can check for footprints, tyreprints, and fingerprints. You'll still know what sort of trace evidence you might find and where.
In truth, even though I've researched forensics, I sometimes forget possible clues. If someone announces to me that they're looking for tyre tracks, I see no reason why they can't roll to find them, whereas if they simply made an Investigation roll, I may not have thought of those tracks.
The same can be said for your Golarion-trotting rogue. Read the various Location books. Know the differences between Riddleport and the Shackles. If you're a wizard with seven languages and a lot of Know Local, read up on the Elf, Dwarf, Halfling, Gnome, and Human companions so you know a fair bit of the culture.
Heck, if you're playing a pirate, perhaps learn your port from your starboard and read up on a lot of Napoleanic fiction (i.e. Horatio Hornblower) so you can start to get a bit of an intuitive feel for the parts of a ship. With some Dungeon Masters, this'll really go well. With others, you might need to make sure that you use new terms in context so they can figure it out until they get an intuitive understanding of it as well.
So there you have it. Do your research, get more from the game, and really get a chance to be who you always wanted to be.