There can be various issues in the manufacturing that can make it hard to get a good straight of grain. Back in the day we would get a friend to help tug the fabric on the diagonal to help straighten... having done a lot of projects with fussy cutting fabrics, I'm not so worried about straight of grain.
Fortunately in modern quilting and processes close is usually good enough. I will typically do a tear across, especially if it is thrift store yardage that I don't know the history. Then I believe in pre-washing anyway part of that is I believe it helps the grain. After the wash, barely dry. and pressing, I fold the fabric in half along the selvedges and try and adjust out any wrinkles or poof -- even if it means the ripped side doesn't match. Then I fold it up again to make it cutting size, using my ironing board as a handy height and shape. Finally I smooth out the folded fabric with my hands, again trying to make any poofs or ripples go away.
When you cut the fabric, you want to unfold especially the first cut to make sure there aren't any Vs at the fold lines. Then about every 3rd-4th cut to make sure you are still straight.
Good luck and don't let it stress you out too much. I second GingerK's advice that sometimes being exactly on grain can cause some issues in itself. And that with printed fabrics sometimes the designs are deliberately "drifted" and don't go straight across the width so I follow the design and figure grain will take care of itself.