How to get greasy film off kitchen cabinets and appliances

Anyone who does a lot of home cooking is familiar with this problem: a greasy film on appliances and cabinets near the stove. While the greasy buildup seems unavoidable, the elbow grease to clean it up is not.
Unfortunately, the more stubborn the stains, the harder it is to remove the grime. While there are many ways that can help remove that layer of greasy film, such as using vinegar or dish soap, one of the tricks lesser known is the technique shown below.
Suppose you just moved into a home where previous tenants left a greasy mess? Perhaps your situation resembles the following.