I love, love, love Lancome liquid ARTLINER! Have used it for many years and it truly has never disappointed me. Easy to use, easy to apply, stays on very well without smudging, and at the end of the day easy to take off. Give it a try.
I use Benefit's Magin Ink liquid liner. It is easy to use for a beginner and lasts all day. It is by far my favorite!
My favorite liquid liner is the Lancome Artliner which has a shorter handle that is slightly easier to hold in your hand when you apply.
I also recommend the Stila Stay All Day Waterproof liner which is easy to hold and gives a super smooth, glide on line.