1. First, you need a good set of oils. You can buy a variety pack...
...or you can pick a few good bottles of multi-purpose oils. Here are my recommendations: Peppermint, Lavender, Frankincense, Tea Tree, and Rosemary. I consider these oils "staples" in my cabinet. I never leave the house without them.
2. Then you need a few different options of carrier oils. You don't want to put oils directly on your skin unless you know your skin can handle it. So get yourself some coconut oil, almond oil, rosehip oil, or avocado oil. Here's a nice set that has rosehip oil and two oil blends that come with it, and here's a set of five different carriers!
3. You need a way to store your oils. They should be kept in blue or amber bottles (if they aren't already), and kept in a cool dark place. A medicine cabinet or a carrier case works well.
Here are two of my cases I use. The wood one stays on my dresser, the travel case is what I take when I'm on the road.
4. A diffuser is the next step. You can put oils in the air with a diffuser or humidifier. Get one specifically designed for essential oils. Here are two of my faves.
5. Make your oils portable. You don't want to take the whole bottle with you, or you could end up with a mess and a lot of wasted money. So put a small amount in roller bottles, or a travel pack. I have my travel keychain pack with me at all times, and it has been a lifesaver!
Good luck, and be sure to check out the benefits of those oils I mentioned above!