The principle methods of working with essential oils in The USA is through inhalation and through massage or other contact work . the third  use which is common in Europe and Asia  is  ingestion  in teas or medicines.This is not usually recommended  in the US  because of potential risks  of over dose and because medicinal effects/value has not been proven according to scientific testing etc..
 I first discovered aromatherapy  through my interest in herbs.  I had worked with herbs for medicine ,cosmetics , culinary , cleansing, spiritual and  decorative purposes  for years. I had herb gardens where ever  I had room to plant some herbs. Because of that I have done a little more work  with including a few oils in  teas and mouth washes  than is usual. I do this with very dilute oils and with great caution and for the most part  I use fresh frozen or dried herbs and occasionally floral waters or hydrosols in  anything that might be ingested.
Essential oils are very very concentrated and with a very few exceptions  must be diluted  before using. lavender and Tea  Tree are two which can be used neat in some cases.

 At first I was skeptical about the value of  essential oils because they they seemed to be  so concentrated and expensive. It seemed easier to work with fresh and dried herbs .
Over the years though, Aromatherapy and essential oils have become a very important part of our household. it is still true that  some herbs are much more accessible fresh or dried or frozen .
Lemon Balm or Melissa  is one of the most expensive hard to find Essential Oils. The Herb Melissa is  very easy to grow, often  invasive in most temperate and Mediterranean climates. It does not dry as well as most herbs but  does freeze well. Melissa, Rose , Heliochrysom, Angelica, Lindon  and Yarrow are among the herbs that are  very expensive and rare as essential oils  that can be relatively easy to find, grow  and work with in herbal form. Currently I do have a very small amount of most of  these precious  oils to work with, though a couple, Yarrow and Angelica I have in such tiny quantity that I really have not dared to use it yet except to smell occasionally. Generally however these are more available to work with in  herbal form.
 Hydrosols  or Floral waters are another way to work with aromatherapy.  A Hydrosol is the water left after the Essential oil is removed after distillation these are fragrant and carry the energy and medicine of the essential oil though it does take much more  for the same effect as a drop or two of the oil might provide.

One of my favorite ways to work with aromatherapy is to add EOs to unscented  shower gel. Several members of my family  have issues with chronic joint pain from arthritis and injuries. I made a shower gel  using a pain relief  blend of oils which has become a great favorite  of family members. One shower gel has lavender , chamomile and honey, it  is excellent for relaxation and for  helping one get to sleep. This is one of the few blends which is suitable for young children. A citrus  and mint gel is a great morning  wake up assistant.

I often put a oil in a diffuser  to suit my needs  though right now my diffuser is broken and I need to get a new one. I  diffuse oils  during Reiki treatments and attunements if the participants O.K. it.  Some people are very sensitive to scent.
What I use varies.  Sandalwood or a blend of Sandalwood and Ylang Ylang are common choices. I have used citrus blends and forest blends and even something a bit spicy from time to time with things like clove or cinnamon.  Sometimes I put a few drops in water and sprinkle it around the carpets, because of the slight possibility that the oil in an diffuser could irritate sensitive eyes. I will choos oils based on the specific issues of the client when that feels right. Uplifting calming and spiritual scents are more favored than  medicinal or sensual scents