Quadrate sampling: Please let me know that which is the best quadrate method to survey grass lands for the herbs, shrub, tree etc. If anybody have more information about it please tell me.

Your question is your answer. Quadrat method is the best. Use 1m x 1m quadrats.

Firstly it is quadrat and not quadrate
When I used to take my my lecture on practicals instructions, I used to tell my students it is quadrat and not quadrate and pl quadrats and not quadrates. Unfortunately even then at least 30 per cent of students would have these wrong spellings in their record books.
The simplest and quickest method of vegetational survey in a large area is line transect method (Line intercept method) where one can calculate percentage coverage of different species in different layers and plot it on a graph sheet also.
One wanting to study vegetational changes along a gradient can use belt transect and lay quadrats (1m x 1m for herbs, 5m x 5m for shrubs, 10m x 10m for trees) at regular intervals to collect desired information.
You may please write your exact requirements to get precise information. Alternately you may get hold of Barbour et al. Terrestrial Plant Ecology, where these methods are discussed in detail. Ecology Workbook by R. Misra is also very useful.

And yes most students also write quadrant as spellings in their record books.

Thanks a lot for correction of the quadrat spelling. I have also experienced the same thing and the reason behind this is Spelling checker of MS Word shows quadrat as incorrect spelling and students change it to quadrate which is shown as correct.

Thanks a lot … I over read that he was to do grass survey so I delimited the size of the quadrat.
…, it depends on the objective of your study if you can use line transects or quadrats.
The percentage cover for trees is not good for vegetation analysis if you wish to do. If you wish to just see what dominant trees lies in the area then line transect may be useful. Line transects may be useful for detecting change, but then there also I always preferred quadrats of 10m x 10m or may be 10m radius circle.
Line transect people tend to use because its easy.
One more way is to do a point centre quadrat method. But all depends on your objectives !!
R.Misra is good book for basics and you must read it. I think every biology student in India should read it. Another twoI would like to recommend would be Mueller – Dombois, D. and H. Ellenberg. 1974. Aims
and methods of vegetation ecology. John Wiley & Sons, New York and Ludwig, J. A. and J. F. Reynolds. 1988. Statistical ecology: a primer on methods and computing. New York. John Wiley and Sons. I followed
these a lot during my PhD work as I also worked on ecology for my thesis. Apart from these I did use other books too, but there is a big list.
For MSWord is saying ‘quadrat’ as wrong, please right click and “add to the dictionary”. Simple :).
My apologies once again.