Whereabouts are you? Some grammar schools are hugely more oversubscribed than others -- the North London schools are typically taking the top 1% of the ability range (I was told this by a head, off the record). So if that's not your child, it's best not to go there. Others are taking more like the top 20-25% of the range, which is always worth a punt.
First step is to find out the format of the papers, ie. is there English and Maths as well, or is it just VR/NVR. Also, are the English and Maths papers multiple choice or written answers?
If the English is written answers (esp if essay) the standard is likely to go someway beyond the usual primary curriculum, so you need to prepare for this in some way. A modicum of specialist input may be required, and lots of practice. Ditto maths, but probably more preparation needed, even if multiple choice. IME selective school maths papers go considerably beyond what most state-educated children will have experienced by the autumn term of Y6. You should aim to have him confident with eg. operations involving fractions as well as simple expressions and equations, squaring/cubing, square roots and cube roots. The Bond papers are a good place to start -- if he can consistently manage one year group above his actual age, you're doing well; if not, some rather more intensive practice is called for. Wrt VR and NVR, you can't really teach these, but they certainly need familiarisation with the different types of questions and doing papers under time pressure. Again, Bond papers are good, but there are other publishers as well, so get hold of a range (Athey, Nelson etc). Bookshops in grammar school areas will usually stock this stuff.
If you're doing it yourself, 15-20 mins a day most days should be enough, if he's doing well. If there are obviously weaknesses, or you're not confident about teaching it yourself, then get some help in.