Aromatic
The most common way to use oils aromatically is through the use of a diffuser so that the molecules can reach a larger area. However, you can also experience the aromatic benefits by simply holding the bottle under your nose or putting a few drops on a cotton ball and placing it nearby.
When I really like the smell of an oil, or if I want to provide the benefits to the whole family at once, I usually turn to my diffuser.
Aromatic use of essential oils is the least likely method to result in negative reactions. However, it would be wise to consult with a medical professional if you intend to use essential oils, particularly with children, pets, if you are pregnant or breastfeeding, or if you have any ongoing health conditions.
Topical
Some essential oils labeled for topical use can be applied "neat," or directly onto the skin for therapeutic effect, while others require dilution with a carrier oil such as grapeseed, coconut oil, epsom salt, or mango butter. The label of each oil will help you decide whether diluting is necessary.
When I'm not a fan of the smell of an oil but still want the benefits it provides, I apply it to the bottoms of my feet and put on socks.
I buy most of my carrier oils from Amazon and Costco. I recommend organic, cold pressed, unrefined oils whenever possible. Avoid water-based and petroleum-based products when you are looking to dilute your oils.
Again, use your best judgement and consult with a medical professional, especially if you are considering use for a child, pet, or if you are pregnant, breastfeeding, or have any ongoing health conditions.
Internal
A few essential oils are appropriate for ingestion. It is very important that you do not consume any oils that are not labeled for internal use and that you keep all oils out of reach of children and pets who may be attracted to the pleasant smell.
Some people will use vegetable-based capsules to ingest the essential oils that are labeled as dietary supplements, or they may be dropped in water or used in cooking to enhance flavor. Remember that essential oils are highly concentrated, and even the "safest" oil can have toxic effects if you go to extremes.
I have limited my internal use simply due to the lack of independent scientific research ensuring the safety of such methods. I recommend that anyone considering internal use of any essential oil use their own best judgement and consult with a medical professional prior to experimenting with this method.
How to Use Essential Oils
There are three different ways to use essential oils: aromatically, topically, and internally. Each oil comes with a label that identifies how it can be used, so you don't have to memorize any complicated charts. Make sure you do read the labels though...not all oils are safe for internal consumption, and some oils can cause skin reactions if not diluted properly!