how to get to qilian shan grassland from xining city?

Well, your time is a little bit tight.
About the transportation, you can take coach at Main Bus Station, and get to Qilian County first.
The schedules are 08:15 to 15:30 with the interval of around an hour. The ticket fare is CNY 58 per person. The duration is 5 to 6 hours for the single way. Then hire a private car to get to the Grassland. It costs CNY 100-200 for the round-trip.

If by rental car, it costs about CNY800-1000 per day. In that case, you can spare more days and visit some other places on the way. If you want to save money, you can share the car with other fellow travelers if you meet some.

thanks for the reply...what if we stay at the qinghai lake area? is it possible to charter a taxi/shared car/taxi from here to qilian mountains and be back in the same day? what would be the costs of such taxis or cars?

Yes, from Qinghai Lake Area, you can hire a private car or share one car with other tourists.
But the distance to qilianshan is not shorter than from XN or maybe even longer if from the main sightseeing site of the Qinghai Lake. So one day's time is also not enough. In that case, you'd better hire a car from directly, which is easier for you.

ok..understood...so if we stay at qilianshan first for one or two days,later would we find buses/chartered taxis/shared cars to come bak to qinghi lake area,incase we want to stay there later...

There are public buses from Qilian area to counties by the lake. But there are only a few schedule each day, which i'm not sure about, you'd better consult the local once upon arrival.
Of course you can hire a car or share one with others for the route, only if you are generous to pay the fare.