I guess what advice I am looking for is how to go about it: can I just show up at their homes or should I take them each out to dinner? Should I bring a token (like a bottle of alcohol)?
If you don't know them well enough to figure out how to interact with them... heh heh heh.
Anyway, Without enough information to go on, I'd simply call them one night when you expect them to be home, and ask if you can come by for a chat. Then go over there and chat.
If she was raised by one dad more than the other, or considers one dad her "dad" (think about who she would call first if she needed help or was injured) then do that dad first. Don't tell either of them which you did first, unless, of course, they ask point blank. Don't bother lying, it'll only cause problems.
Assert that you are asking for their blessing for your marraige - not permission. Don't use any language that suggests that they have a say at all - merely that you 1) want them to understand your intentions and 2) want them to accept you into their family as your family accepts their daughter into yours.
They will either give you an answer right then, or they won't give you their blessing. If they hesitate and want "time to think about it" just chalk it up to them not liking the idea but not wanting to reject you outright. Expect them to ruin the surprise for your intended.
And ignore all that, if that's the case. You did what you wanted, and it's up to them whether they accept and support your union going forward, and if they don't it's their loss. Usually they wise up by the time you have children.
I'd want to surprise my family with the news
Some guys like to ask for the blessing prior to getting engaged, and I suspect that you'd probably give your guy that one thing if it was truly important to him.
Likewise, if you make it clear that you would be offended if he did that, he'd probably back off from that tradition.
I got engaged to my wife, and that evening went to her parent's and surprised them with the news together. I don't see why you couldn't do that, but you should make it clear to your boyfriend early enough in a relationship so you don't get burned because he wants to "do it right."
My wife is very, very social, and so while I didn't specifically plan for it to occur this way, I'm quite certain she's glad she was able to be there for the surprise, and participate in the emotional visit with her father and mother. It's not an issue of ownership or control at all - it's merely the desire to be present for such an important announcement to the people you love.