I have used the tire plug kit to plug nail holes in my tires twice in the past, both tires lasted until they worn out, no leak so I think I did an ok job. However each time it was super hard to push the plug into the hole, took me a lot of time, bruised... Does anyone know of any tips/tricks, or may be tools, a special clamp or something to help with that? Thank you!

 

If you're talking about the older gooey rope-style plugs, the only thing that helps is to use the reamer tool more are wiggle it around as you're reaming the hole.
If you want a better plug and an easier way to install it, pick up one of these kits:

https://www.ebay.com/itm/Stop-Go-Poc...e+plugger.TRS0

They install much easier than the old style plugs and because of the mushroom head design they never leak or pull out. I've been using them for 5-6 years now on both my motorcycles and cars and I've never had one fail.