Allowed uses on a property are dictated by the zone. Some uses have zone specific standards, which means that certain regulations, such as minimum site area, may dictate further if a use is allowed. Non-residential Commercial uses typically require use permits from the Planning Division. There are two types of use permits, a Basic Use and a Conditional Use Permit.
Start by confirming what category the proposed use falls under by referencing LDR Sec. 6.1.2 Classification of Uses. Once you have figured that out, you can reference the Use Schedule in Sec. 6.1.1
The table will indicate if a use is allowed in a zone by right (i.e. no use permits are required) with a "Y", allowed with a Basic Use Permit with a "B", allowed with a Conditional Use Permit with a "C". If the section is blank, that means that use is prohibited within that specific zone. There is not a relief process in the LDRs which would allow a use in a zone where it is not permitted by the Use Schedule. Again, use-specific as well as zone-specific standards may involve additional requirements or restrictions. Those are typically listed at the end of the zone article in the LDRs, or in the use standards in Article 6.
Basic Use Permit application checklist can be viewed here.
Conditional Use Permit application checklist can be viewed here.
Both applications use the general Planning Permit Application.