The need for a Special Land Use permit is determined by the use of the property and the district of the property. First, find the district that you are in by finding your property on the zoning map, then look up the section in the ordinance that governs your district and find that a like use. That use will either be "permitted" or "subject to special conditions". If the use falls under the latter, "subject to special conditions", then most likely a Special Land Use permit is needed.
The Special Land Use process involves two meetings at Planning Commission, one to set the public hearing and one to hold the public hearing, and one trip to City Council for final approval. The process usually takes 2-3 months if the matter is not tabled.