You can add an individual record from any search or browse results to the basket simply by clicking on the record (assuming that the icon to the right indicates that it is available).
You can also use the check boxes to the left of the search or browse results to select more than one record and then click on "Send Selected to Basket" to do just that. Currently there is a limit of sending no more than 100 records to the basket. You can also use the "All" and "None" links to select all or no records with one click.
You can remove records individually from your basket by clicking the 
icon in the upper right corner or by clear your basket (remove all records in it) by clicking on the scissors 
icon.
Additionally, you can remove a record from your basket when you close it after making edits by selecting the "Save and Release" option in the pop-up.
