Your plumeria has three basic needs:
If you provide these, they will reward you with many lovely blooms.
Water is very important to your plumeria. Your plant must have enough water in the summer months. Without adequate water your Plumeria will go into a suspended state or dormancy. The plant will abort flower stalks and the leaves will drop. Allow Plumerias to go dry in between watering, then a deep soaking is in order. Watering depends on the daytime temperature and humidity, a good balance is essential. Plumerias do not like standing water, do not use a catch bowl under a potted Plumeria.
When the plant drops its leaves in the cool fall and winter months, DO NOT WATER. Give it only enough water is necessary to keep the soil slightly moist. Mist the stem if it begins to look wrinkled. If the temperature in your environment drops to 32º F, the plant may be bare rooted and stored in a freeze-protected area. The plant can be replanted in the spring and will do well.
6 to 8 hours of direct sunlight is needed for good blooming of your plumeria. Some varieties require some shade from the hot inland sun in the summer months.This is a highly loaded topic. A beginner should start with a moderate, balanced fertilizer, such as a 3-12-12. The theory is that high phosphorus numbers found in "bloom buster" fertilizers create short-term blooms at the expense of the long-term health of the plant. Apply at a rate of 1 pound per inch of trunk diameter, spread evenly to the drip line of the plant. The best fertilizer is the one that works for you. Follow the directions on the bottle, and don't hesitate to use less than the directions indicate.
Some folks feel that to encourage blooming, plumerias need a high phosphorus fertilizer. Refer to the N-P-K numbers on the bag. The P is the Phosphorus content. Superbloom, Superphosphate and Hi-Bloom are some examples. You can use a 10-52-10 water soluble fertilizer at a rate of 1 to 2 teaspoons per gallon of water. A weaker solution and using it more often gives very good results if your plants are in pots. Here's a care calendar for zones 9-10 if you're interested in following the high phosphorus philosophy: High Phosphorus Fertilizing and Care calendar for Zone 9 and 10 (PDF, new tab) Again, this has become controversial in recent years since some feel it sacrifices the long-term health of the plant for short-term blooms.