To start, navigate to Catalog > Manage Products in the admin side.
You'll be taken to a screen showing a grid with your products.
Along the top of that grid, you'll see empty fields which you can use to filter out products.
For this example, I'm going to filter products based on name.
Notice that typing in "test" and clicking "Search" in the upper right hand area results in displaying products with the word "test" in its name.
You can apply this logic for things like SKU or any of the other fields you can see in the columns.
I'll be editting both of these products, and to do so, we'll check them off under the "Any" column.
After checking these items off, navigate to "Actions", select "Update Attributes" and then click "Submit".
You'll be taken to a screen where you'll see a list of attributes.
From here, you'll find the attribute you want to update. Notice that there's a checkbox next to the attribute. This is sort of a fail-safe for Magento. ONLY the attributes that are checked off will be updated.
For this example, we'll enter the new data and check off the "Weight" attribute.
After you've made your changes, hit "Save" in the upper right.
And your products should be updated!