A lot of people ask me what's involved in changing the oil on their Miata. This guide from iFixit.com goes step by step with lots of high quality photos to follow along.
Make sure your Miata is secure when jacked up. It may slip off and cause injury!
Don't tighten the drain plug past 'snug'. Over-tightening can strip or crack the oil pan!
Allow 12-24 hours for your old filter to completely drain. Take your old oil and filter to a recycling facility. Most auto parts stores and repair shops accept these at no charge to you. In addition, some cities and/or counties have a service where they will collect used oil and filters from your home. For more information, see the American Petroleum Institute's web page on used motor oil collection and recycling.
Full guide here: https://www.ifixit.com/Guide/1990+1991+1992+1993+1994+1995+1996+1997+Mazda+Miata+Oil+Change/6337