There are two different ways to approach this, depending on if the attribute value will be the same for many/all of the assets (such as a drop down, keyword picker fields) or if the value may be different for each asset (e.g. notes).
If the values will be different:
Go to Batch Update -> Start a new batch update. Select your search criteria, and click 'search'. All the appropriate assets will load up one at a time in edit mode, allowing you to edit the appropriate field. Click 'Save and Continue' to move onto the next asset.
You are able to have 100 assets in each batch update.
If the values will be the same for many, if not all assets:
Go to Batch Update -> Bulk Update -> Start a new bulk update.
Select your search criteria, and click 'Search'. The system will let you know how many assets were returned by your search results, and then you can handpick which assets you would like to update by clicking 'Select assets in batch for update'.
Then click 'Run an update on this batch'.
You will then be asked to select the attribute that you are changing. Tick the box to indicate that this attribute is changing, and then enter the value as necessary. Keep in mind that all assets in your batch will be updated with the same changing information.
Select 'start update' to update the assets accordingly.