I added a sharepoint list on a different page, but the search box for the list does not appear.
Edit the page > edit the list web part settings by checking the checkbox and select "edit webpart" from the dropdown menu.
Look under the tab "miscellaneous", there should be a checkbox to toggle show/hide for the list search box.
Or if you are using a different style for the list view, that might be the problem as some of the styles are pure OOTB styles from SharePoint 2010. If so, the search box won't be available with that certain style.