Logic is a really good quality toothpaste. It's comes with a finger brush too so you don't have to buy a separate one.
As pp said, start slowly using some toothpaste on your finger and get your dog used to you moving his/her lips and touching the gums - if teeth haven't been cleaned before the gums might be a bit tender so go gently - and very gradually work your way towards using the brush.
It takes a long time to get most dogs used to having their teeth cleaned, my dog is 12 years old and she still has issues with it, although she does love the flavour and as soon as I say we're going to clean her teeth - I do it each night before she goes to bed - she jumps on the sofa and sits waiting, like the absolutely best girl, for me to attempt to clean them.
The vet says they're looking good so we must be doing something right.
If the dog's teeth are in a bad way though, brushing won't really have much impact and it might be necessary to have a scale and polish under anaesthetic to get them clean before you start cleaning each day.
And to answer your question, no it's nothing like cleaning children's teeth, unfortunately, unless your child enthusiastically waves his/her head around the whole time you're trying to clean their teeth.