I'm both pretty new at FM and American, but somehow I stumbled into a strange treble in Year Two 2011-2012: League Cup, FA Cup, Champions' League. Here's a few things I learned/did:
I kept my staff together until I got tired of Joe Jordan always disagreeing with Tim Sherwood. So I, probably mistakenly, fired Jordan. I picked up some Venus guy as assistant coach, and only much later starting paying attention to the ability levels of coaches (e.g. tactics 20). I noticed about 18 months in that I had no fitness coach (after he was poached and I didn't replace him). Mistakes were made.
In games, I ended up letting Sherwood ALWAYS pick the starters and I just filled in the subs. I almost always went with the formation suggested by Sherwood. Venus, too, always seemed to disagree but has started agreeing more and more recently.
I made the huge mistake of spending 24 million or so on Luis Suarez, who then proceeded to dive alot, miss shots and lead me to something like a 4-2-4 league start. I finally bit the bullet and was able to dump him on Valencia (IIRC) for 18 million or so. My popularity skyrocketed. We righted the ship a bit and ended up a distant 6th, only qualifying for Champions' League again by winning the **** thing.
So I struggled through the existent striker force of Pav, Keane, Crouch and somehow muddled through.
Perhaps the biggest thing was lucking into several good draws (lots of home league/FA Cup matches, a CL Group with Sevilla top seed, etc.) I didn't have a really tough CL game until Bayern in the Quarters...then it was All-England through Gunners and MUFC in the Final. It was Sunderland in the FA Cup Final and Bolton in the League Cup (IIRC). No complaints there...
I kept the squad pretty much intact, adding only Alou Diarra, Sebastian Corchia and some other youngsters (my plan is to keep playing Spurs for quite some time), but mainly it's been a matter of NOT getting rid of folks even they bother me to "play for a bigger team" (Bale, Corluka, etc.) Bale just bothered me about this AFTER we won this treble. Now he's turned down my latest contract extension offer (what a virtual jerk he is).
Yes it took far too much time, and Yes I'm a little embarrassed about the time-sink and the thrill of winning this treble...but there it is. I think I'll try a network game or two given my new over-sized ego. Hubris is a beautiful thing.
P.S.: After my Suarez debacle, I avoid the Dzekos and Cassanos of the world. I picked up Zarate and even that might be too much ego/money/diva..for me at least. Managing strikers in the real world must be such a royal pain...