Summarize:

Each denomination has its own guidelines governing the way that oil is blessed for anointing purposes, as well as the way that anointing oil is used.  The most common restriction regards who may bless or anoint the oil. In some denominations, such as in Catholicism, only a priest or similar clergyman can bless the oil. Some denominations even limit which clergymen are authorized to consecrate oil.  It is also important to note that some denominations, such as the Latter Day Saints, also have guidelines and laws concerning what oil should be consecrated and how it can be used afterward. You can use any type of olive oil that is available. However, it should be olive oil instead of another type of oil since it has greater traditional and biblical significance because it is mentioned in religious texts.  Unless you are told otherwise by a religious authority, it is not necessary to buy special oil for anointing.  Extra-virgin cold-pressed olive oil is the purest variety available, so many people prefer to use that when shopping for an anointing oil. You can find this oil in the vast majority of grocery stores. If desired, you can buy scented olive oil from a religious or secular store. Oil that has been perfumed with frankincense and myrrh is both popular and spiritually significant because they are referenced in the bible. Find a small vial, bottle, or other container that you like the look of or that has special meaning for you. It needs to have a lid that closes tightly and does not leak. Make sure it is clean and the pour the olive oil straight into this container. This oil will become the anointing oil.  You can buy a special oil stock at a religious bookstore or online, or you could use any small bottle. The most common vial is a short metal container with a screw-on lid, with a sponge placed inside to help hold the oil in. However, less expensive plastic oil stocks are also available. Even a brown glass bottle with a dropper or a roller cap could be used. While you can anoint plain olive oil, some people add essential oils that have religious significance. Anointing the body with perfumed oil was once used to refresh the body. If done to someone else, the act was considered one of hospitality. The oils used can vary but consider adding one drop of each of these, as they are mentioned in religious texts, such as the bible:  Myrrh Cinnamon Cassia Calamus As long as your denomination does not prohibit it, you can usually pray a blessing over the oil on your own without the help of a religious authority figure. The prayer should be firm and one made in good faith.  The prayer you use must ask God to bless and cleanse the oil, so that it can be used for the sake of God's glory. For instance, the prayer might be something like, "God, I pray that you anoint this oil in Your heavenly name. I pray that You cleanse it of any defilement in it or upon it, and that You make it holy for the work of Your glory. May this be done in the name of the Father, the Son, and the Holy Spirit. Amen." The best way to keep the oil fresh is to store it at room temperature. Put the container in a dark area when you are not using it, such as a cupboard. Refrigeration is not recommended. If you refrigerate the oil, it will start to look cloudy. This is not harmful, though, and the oil can still be used even if it has gotten cloudy.
Check with your judicatory or a religious authority for specifics. Purchase olive oil at your local grocery store or online retailer. Fill up a small, special container with oil. Add essential oils to the olive oil, if you like. Pray a blessing over the oil. Store the oil at room temperature.