We bought 2 grape plants last year. When they grew, they yielded each a tiny bunch of grapes but this year, each plant has more than ten bunches of tiny little fruits. My query is how do I look after them to ensure I can maximize the growth of grapes and approximately how long does it take to grow to maximum size before harvesting? Is there any special things I must do? Thanks.
There is, not surprisingly, a whole lot to know about growing grapes. Much advice will be based on the kind of grapes you have, and the area in which you live. Since you didn't provide either of those bits of information, the best I can do is direct you to some basic general articles: https://www.gardeningknowhow.com/edible/fruits/grapes/growing-grapevines.htm
Also I urge you to make use of the resources provided by your communities. That would be the county extension service in the US, and the master gardener program in the UK, Canada, and Australia. Other places you can ask for assistance at any botanical garden near you.