How can grandparents get custody of a grandchild that they have taken care of for a year?

Yes, I think you need to talk to an attorney about this.  It sounds to me as if you have a fairly good case, to ask the court to award you legal custody, but it's not something you could do yourself.  There's a fair amount of specific rules to be followed, including giving notice of what you're doing to your daughter and to the child's father, and the child protective services agency might also get involved.

It's possible that you could get full custody, but I think that what is more likely is partial custody, with your daughter, or temporary custody, to be revisited in another year or two.  The fact that the child has been with you for most of her life will work in your favor.  Cases like this tend to be very sensitive to the detailed facts, and presenting those facts in the most effective way is one of the main reasons you need a lawyer here.