If you grab the Falco at 0%, use Fthrow twice instead of Uthrow. At 0-5~%, Fthrow puts Falco right into a landing position so you can grab again (at higher percents they hit the ground and can techroll and whatnot). Then proceed to Uthrow, and up to 30~%, you simply have to turn and grab, no dash needed. You can then chaingrab to 40~%, but you have to dash to the side they DI to catch them. If they don't DI, dashdance -> JC grab. Once you're around 40~% (better below than above), Uthrow -> Utilt -> grab.
At this point, there's a couple things to do. If the Falco is DI'ing to the side you can catch them with a tipper Fsmash. If not, you can USmash, Utilt, Uair, -> some form of ****. Just experiment and you'll come up with combos.
Other than that, mastering CGing is simply a matter of practicing the timing and learning to follow DI. It'll come with practice, just don't give up too quickly.