Here are the steps to change from oil base paint to latex. They all must be followed or the latex paint will peel.
You didn't specify if your trim is interior or exterior, so I will give you a quick breakdown of both. The process of converting from an oil base paint to latex is a fairly easy one, plus many of the steps are the same for both interior and exterior trim.
Step 1- Clean the Surface
For exterior trim this can be simply washing with a garden hose and a stiff scrub brush or for very dirty wood using a pressure washer and mild soap. For interior trim usually washing with a mild soap and rinsing with clean water is enough. For an even better washing try using a deglossing compound like Paso. It stinks really bad but does a great job.
Step 2- Remove Loose Paint
If any paint is peeling or bubbled it must be removed. This involves scraping first then using sandpaper to level the edges, "feathering". You can use a palm sander, if you have one, to save time and effort. Generally, I like to use an aggressive grit first, like 60 or 80 grit, and then finish with 120 or 150 grit.
The idea is to blend the edges of the paint and the area with the surrounding surface. Basically you need a smooth surface without a lot of large scratches from the sanding. After sanding remove the dust. This can be accomplished by vacuuming or rinsing the surface with water. Paso and a clean rag can also be used.
Step 3- Priming
This is the most important step when converting from oil base paint to latex. I prefer oil base primers for this type of painting. A good brand is Zinsser Cover Stain. It sticks really well and dries fast. Another good primer and readily available is Kilz Oil Base. The manufactures of these primers states "recoat in 1 hour" but give it a few hours, 2-3.
If you are painting exterior trim make sure the primer is suitable for exterior use. Not all primers can be used outside.
Now you can paint. Choose a top quality 100% acrylic paint. Personally I like Kelly-Moore and Benjamin Moore. The best place to find the best paints is at your local paint store.