The OED costs $100/year for US residents or £100/year for everyone else [0] but you can often get access through a library. The San Francisco Public Library has a proxy you can use if you have a library card there [1].
[0]: https://global.oup.com/academic/product/oxford-english-dicti...
Another great writing resource is etymonline.com, which gives a bare definition along with a full etymology drawn from different sources.
Most people don't need the full OED and should probably just buy one of the smaller Oxford dictionaries. The Concise Oxford English Dictionary is an excellent single-volume dictionary of modern English based on the Oxford Dictionary of English (which is not the same as the Oxford English Dictionary. The OED is a historical dictionary, while the ODE is a dictionary of contemporary English).