You'll notice that storks often fly by with moneybags, which drop if you tap them. Typically, the faster the stork, the more money that you'll earn from the bags. Eagles often fly by at very high speed, changing directions as they go, carrying moneybags as well. If you tap on them before they fly off the screen, you will get a HUGE money reward, worth far more than both the storks and even the random gifts.
When you hit a high enough farm value, you'll be able to unlock the next type of wool. Each different type of wool is worth significantly more per sheared bit; however, if you just got back from being offline for a long time, don't upgrade to the next wool up just yet. Check if you can upgrade by two wool tiers instead. If you're close, keep upgrading and tapping until you get there so that you can skip over a type of wool.
As you get farther into the game and a number of wool upgrades under your belt, you will be able to unlock prestiging. In order to prestige, you have to completely reset all of your progress, but you get an earnings multiplier. In addition, your permits and golden wool, as well as all of your purchases, will remain from before.
If you want to take the tapping out of the equation and make this a completely idle game, then purchase the upgrades that automate cloning in the shearing centers and just let the game go. Or, if you really want to speed up the adding of sheep to your shearing centers, then tap with more than one finger at a time. The bigger the device, the more fingers that you can tap with, so if you are playing on a tablet, a 7s or a Galaxy Note 8, for example, then you can earn sheep at a very high speed.
If you really want to speed up the tapping, go down to the cloning house, then zoom in as far as you can. Tap with two fingers on the cloning house and three or four fingers (depending on phone and finger size) on the sheep bar, and mash as fast as you can. This will get the tapping done extremely quickly.