Lets face the facts.... lager is delicious. I've brewed about 8 batches of ale, stout, and mead since I've started my home brewing adventure but I'm clueless about lager. I attempted a big batch of Oktoberfest following a kit as close to the letter as possible last year, but it came out like garbage. I just brewed following the instructions in the kits, and when it came time to secondary, I simply put it in a spare garage fridge at the highest temp I could, which was about 40 or so degrees. I waited patiently for about 3 weeks, bottled them, and put them right back in the fridge. When I opened up the first bottle it smelled skunky and had floaters in it. Dumped it. Second bottle the same. Popped open a few more, all the same. Completely undrinkable.
What did I do wrong and how should I go about in the future trying to make a lager with the bare bones set up?
Something to consider (though I don't think it has to do with the floaters or the skunkiness) is to pitch a LOT of yeast for lagers. Its very hard to overpitch. Look at how much you need for the beer, then add a little extra on top.
In direct response to your question, it could just be some very basic stuff. For the floaters, make sure you are whirlpooling your kettle before siphoning off the wort. This will help keep trub in the kettle, and not in your fermenter. Some (including me) think its a good thing to get at least some of the trub into the fermenter, but if there's too much, its more difficult to siphon the beer off the trub at the bottom of the fermenter. be very careful when transferring beer to your bottling bucket and leave a little beer at the bottom of the fermenter to make sure you don't get a ton of trub in your bucket.
Skunkiness is typically due to the beer being lightstuck. Make sure that your hops are in a dark, cool place for storage, and same with the fermenter. if you are using clear or green bottles, keep them in the dark too until you are ready to chill them for drinking.
Sometimes those kits don't have the greatest ingredients. The yeast in particular tend to be not the greatest in my experience. I always say the best way to improve those kits is to throw out the yeast pack it comes with and get some fresher stuff.
Some of the stuff in the kit could have been sitting around for a while. I always recommend buying the ingredients from your LHBS or if you don't have one, order from a reputable online source.
Infection is always a possibility, but I feel like this is more obvious overall as opposed to the things you talked about.
Hope that helps!