Cutting veg' needn't be difficult, it can be easy.
You need a good sharp knife.
It's worth having even only one knife with a decent stiff blade that can be resharpened. I found a Sabatier 3-pack on a market for 15 pounds (bargain!) I won't claim that Sabatier are the best, but they're good enough. If your knife isn't sharp you'll have trouble using it. Blunt knives are for spreading butter and such, not vegetable preparation.
(If you watch the videos, with their cheesy-tunes, notice how easily the knife goes through the onions - little force needed)
You also need a good solid surface to work on, I'm sure you know what a chopping board looks like, mine is made of wood.
If you have the option, choose onions which are hard / firm, softness is not good in onions.
Good onions should have little or no smell (before you peel them) - if they smell, they're not good.
Also check for visible signs of damage, if stored properly, onions should be dry on the outside and free from mould.
(I was a bit shaky due to illness, but I managed not to slice myself)