For your safety know that you can quickly delete your search history . This can be done easily by pressing CTRL then H select "clear search history".

Delete Internet Browsing History
for Internet Explorer

If you are accessing websites, (Such as the Women's Center website or an online banking website) then you can delete your history afterwards so that it cannot be tracked

Step 1: After you have finished your search, return to either your computers homepage or google

Step 2: Click on 'tools' 

Step 3: You will be presented with a drop down menu, click on 'Internet Options' 

Step 4: Click 'delete..'

Step 5: You will be presented with a list, select all that you would like to delete