can I prevent my computer from keeping a history of where I browse?

Yes Manisha, 

You can delete the temporary internet files, cache files and cookies from your system. This would prevent the computer by showing the history.

 If you are using Internet Explorer:
1. Go to Tools >> Internet Options.
2. There in General tab,  second section Check ON the Delete Browsing History On Exit. 

This would help you prevent the storage of the history.

Go to toolbox and slect number of days for which you want to keep history. Opt for zero days. Also before logging out delete history using Tools- option.

The best thing you can do is to download Ccleaner 2.35 and index dat analyzer 2.5

The above mentioned software clears the browsing data, your dat location file , cookies , and all the temporary file ,recently typed URLs and all the data which can track you.

If you use the other method of clear recent history there are many chances of being tracked.

you can browse in incognito mode

Yes it is possible to delete history.

You can delete the browsing history after completing your task.