I do mine in the food processor - it ends up a sort of coarse pulp. I do add water and sometimes tomato juice - I find it makes it easier to deal with.
I use whatever veg I have at the time really but never onion or potatoes. I do put in a couple of cloves of garlic to each batch and a scoop of Keeper's Mix.
Other than that I use any of the following:
Carrots, parsnips, swede, brocolli, apple, banana, courgette, tomatoes, spinach, sprouts, peas (including the pod), celery. It is up to you what you use and you will learn what your pup likes. Coco loves carrots so that normally forms the bulk of it - probably 50% of each batch.
I then pour it into ice cube trays and freeze, then tip the cubes into a big bag and take out one or two cubes at a time to thaw. I don't feed veg with every meal - usually only when Coco has a mince or offall meal so probably about half the time overall.