I think we can all agree that without Egg Toss, Yoshi would be one of the bottom characters in the game.
This move makes playing Yoshi much much easier, its very versatile and often the only real option you have. The eggs allow Yoshi far more control over the field and over how the game plays out, they outcamp many characters and can be deadly for characters without a projectile of their own. We can keep enemies at bay, clear a safe passage back onto the stage, excellent for spacing with ETS, approaching and they even help us recover.
But all of these benefits mean that you often see Yoshis overestimating the move and getting punished for it, a lot. There is a lot of ending lag on this move which can make it pretty ineffective against speedy characters coupled with the fact that the eggs are slow and easily avoided, not to mention they are rather lacking in blast radious. The only reason you should be using the egg toss up close is with ETS to dodge when you know it can work.
ETS is a great way to both increase and decrease the gap between you and the opponant, some characters can be very effectively camped with eggs along with pivot grabs and Dtilts. But when using ETS remember that it isn't always the best way to throw eggs, if space is not imortant then standing egg toss is faster to spam eggs. Approaching is also another great use of ETS against some characters, the biggest problem comes however from how easy it is to powershield the eggs. Good spacing is essential, mixing up approaching with retreating eggs. When you get in close, ETS > DT > Dtilt or Jab can work, just a shame about how much lag egg toss has.
Whilst ETS is great against ground opponants, where it really shines is in taking down airborn foes. Because the Egg Toss is so manuverable it covers pretty much anywhere above the stage. Characters who spend a lot of time in the air such as Wario, Marth or Jigglypuff can really suffer from having their movement and approaches messed up by eggs, or having to AD eggs. Which brings me onto a really great use of Egg Toss, Baiting the AD. As well all know, getting in the Usmash or Uair for a kill can be a tall order and we are all painfully aware of difficultys when it comes to killing with Yoshi. This is why egg toss is your best friend. Most enemies are going to AD an incoming egg in the air, and this is your chance to capitalize with a rising Uair or SH Uair/Usmash if they are low enough.
Another new thing I have been trying is wavebouncing the egg toss, really great for spacing. SHing toward them and wavebouncing the EggToss back can often causes them to think they can punish the toss and go for that over avoiding the egg.
Then of course you have ECE and using eggs off the edge, the primary use is clearing a path back to the stage which is very important for Yoshi being as gimpable as he is. ECE is amazing against people haven't learnt to overcome it.
Thats about all I have time to write.