In general, warm paint colors work well with oak trim. Warm brown, honey, gold, beige and even a muted, moss green work. Look for paint colors with more red or yellow than blue or green in the base. Many paint companies label paint in warm and cool categories.
The best way to select a paint is to take a bit of the oak trim with you to the paint store. Hold it next to the paint samples, and you'll quickly find colors that complement the trim. Narrow your selection to three colors, and buy small sample jars for each paint color. Brush the samples on the walls in several areas of the room and live with them for a day or two. The colors may appear slightly different, based on the time of day and lighting. Select the color that appeals to you, regardless of changes in lighting.
Always apply primer before painting, especially if you've chosen a color that's darker than a basic neutral. The primer will ensure an even, smooth application and true color. The paint will last longer, as well. Paint some of the woodwork with a complementary color to add contrast to the oak. For example, if you've chosen a warm honey for the walls, paint a door or built-in entertainment center moss green or warm brown.
If your oak trim is inexpensive, damaged or dated, you may be better off painting it white or cream. The fastest way to paint trim is to remove it and set it on saw horses in the garage. Sand it lightly, and repair damaged areas. Rent a paint sprayer and spray it, first with a primer and then with a durable enamel paint. Number the pieces of trim as you remove them from the wall so you'll know where they go when it's time to replace them. You'll get a clean, professional look, and you'll have many options when it comes to choosing wall paint.