A tip in general for making paste out of anything is to use table or sea salt. Obviously do not add to much a tiny pinch goes a long way. Salt adds an extra surface area which chopping up ingredients and kind of works like a mini grater.
To make garlic paste in particular, I try to chop the garlic into thin slices longitudinally, while maintaining its shape. Then I slice it latitudinally again. I flatten the garlic with the flat area of the knife and then I add the salt at this point and then chop again. And repeat over and over again until I receive my satisfied texture.