Is it a rooted plant or a cutting" as this makes the way you handle it change.

Look at the list of subjects under Plumeria Care at the site listed below.

Here is a link that might be useful: The Plumeria Society of America

tdogdad,
It has roots, I think. I bought it at Walmart.

How long can I keep it in the pot?
I keep it indoors in a partial sun window. No shade on window.

I'm so excited to grow one of these and thank you for your help!

You can keep them in pots forever, but the pots will get bigger in time. When a plant is top heavy and blows over constantly you need to pot up or sink another same size plastic pot in the ground and set it in. When a plumeria becomes root bound, you can cut an inch or two around the inside of the pot, remove the old roots and restart the plant in fresh soil mix. This is best done in February as the plant prepares to exit dormancy. Generally, you can go several years in a one gallon black plastic pot (no clay pots unless glazed inside) or a size of 18-24". The five gallon will go to 4-5' if balanced. A 7 or 15 gal you begin to branch prune or stem prune and then root prune every 2-5 years. These are general guidelines and depend on the growth rates, size and balance of growth. I stake and tie my plants and branches to control the balance and force plants more up than out. I recommend you put your plant outside as long as the evening temperatures are averaging 60. You can put your plant outside in the day and bring inside in the night for most of the year in SoCal. I have several hundred plants so I just leave them outside all year with some rare frost damage in Dec-Feb once in awhile (2007 was harsh).
Since your plant probably has roots, drench water it (pour water in until it is flowing out the bottom) Then let it dry out for several days. Go to home depot and get some superthrive (in indoor plant area) and look for a cheap water meter (also at most nurseries) Water when meter reads dry. Add a few drops of ST to each watering and mist your leaves in the morning with a spray bottle. Don't freak when lower leaves turn yellow. pick off. By Nov/Dec your plant will drop all leaves and go dormant (little or no water needed until Mar. Start watering in March and pick up some fertilizer (you will find a wide variety of opinions here including epsoms salts, sulpo mag, spray n grow, calcium products, various formulas, etc) Search this forum and read up. Welcome to the world or plumiaholics. Bill