I need to disable item deletion for "users" in one list, but they need to be able to add new items. Any suggestions?
I'll just expand on Allen Bai's answer - he's right. If you are unfamiliar with how to 'create a custom permission based on Contribute' then reference this link on Microsoft's website.
You need to create a custom group, name it 'Contribute not delete', so that you and others will know what this group is for. As you see in the picture below, the user group 'Contribute' has a collection of permissions - you'll notice that the Contribute group has 'Delete' as a permissions.
The best practise is to create a new group, don't change the default group!
Create new permission
A new permission is actually a collection of individual permissions - but the collection of permissions has a name - this name is the group name. Anyway...go to:
Site settings>Site Permissions>Permission Levels>Add a Permission Level
What do you select and what should not be selected? To answer this - take a look at the existing 'Contribute' group - make a note of all the individual permissions selected here. You need to select all of the same ones except delete when you create your new group.
For your own peace of mind you might like to ask a friendly user to test that they can create new items, but not delete items.
Create "ContributeNoDelete" Permission. And Create Group with "ContributeNoDelete" permission.
Please see below link to create "ContributeNoDelete" Permission
Please do comment if anything needed from my side.