As pointed out above, the key to this is having the confirmation number/booking code for each partner airline (different airlines use different terms for this, but they all have one - confirmation number, booking code, reference number, PNR, whatever - if in doubt try any of these terms). The various airlines' systems do not speak the same language, so the code for your United reservation may be (usually is) completely useless for the partner airline's system.
You booked using United FF miles, so start with United. Log in to their website using your FF account. Click "My Trips". Your flights should be listed there - click the one you need info on. While you're there, note the United Confirmation Number - keep this and have it handy, you might need it in a pinch. There should be a link for "Other confirmation numbers" or some wording to this effect (I don't have it in front of me right now). That's where you will find the code for the partner airline; it's usually (not always) a 6 digit code. Record this partner airline confirmation code - it is the key to everything you need to do with that airline. If you can't find it on the United website, call United and ask them for it - they should be able to give it to you (try the website first though, you will avoid the long phone hold).
You will want to have this code handy whenever you deal with the airline you're flying on - and not to put too fine a point on it, but once your flights are booked, you are done dealing with United: when you deal with the airline you're actually flying, leave United out of the conversation, any mention of that will just confuse them and complicate things for you.
I can't help you with either Aer Lingus or Swiss, you will need to try them yourself. For most airline partners, just go to their website (remember, you're done with United), look for a link like "Manage my booking" (almost every airline has this on their website). You will usually need to enter your confirmation code (for that airline) and your surname. Once you do that, you should be able to access your booking. For most (though not all) airlines, you can then pick seats, check in online (usually within 48 hours - exact details vary) and perform other minor tasks. Picking seats is most important. Try to do this ASAP if you can. If you can't, call the airline (their US office, find the contact number buried on their website) and ask them about picking seats.
This should work for most airlines. A few airlines have weird rules that restrict how/when you can pick seats (eg: can only pick seats within 90 days before the flight, or within 48 hours of departure, etc.). If you have trouble, call and ask about this. Only a few require you to do this upon arrival at the airport (which really sucks). Most likely you can do this all on the website once you have the necessary confirmation code. Picking seats once you get to the airport is almost a guarantee you will get a really bad seat, so try hard to pick your seat ASAP, not at the airport when the only seats available may be a middle seat in a non-reclining row next to a stinky toilet.
Good luck.