Entry level, sports model, circa 1980/1981. Second from the bottom of the line. Miyata is Japan's oldest bicycle manufacturer and were very popular in the USA during the 1980s. During this period they were arguably the best mass production manufacturer of bicycles. The bicycles are excellent value at their respective price points due to excellent design, manufacturing and assembly practices. Miyata's philosphy of producing the best bicycles, led them to establish their own tubing facility, the only manufacturer to do so.
Since you're relatively new, the term slipping could be slipping (i.e slips out of gear, down to the next smallest gog) or skipping (i.e chain jumps off cog, but remains on the same cog).
Slipping usually happens because the screw that holds the shift lever needs a slight tightening. This puts pressure on a friction plate that counteracts the return spring in the rear derailleur. If you tighten it too much it will be hard to shift, so it will probably require some trial and error to get the right balance.
Skipping can occuir for a number of reasons. including a tight link in the chain. If you raise the rear wheel and pedal slowly, you should notice a kink in the chain. It is most noticeable when using the smallest cog on the back, as this is when the link has to pivot the most. If you notice a tight link, apply some light oil, grab the adjacent links and flex the chain sideways, numerous times. This will generally loosens the link.
Skipping can also happen with a worn chain and/or cog. Often people tended to ride their bicycles primarily in one gear. The chain and cog would wear, to point that shifting to infrequently used (i.e. unworn) cog would causing skipping. Installation of a new chain would solve the problem of skipping on the unworn cogs but would result in skipping on the heavily used cog. With a heavily worn chain and/or cogs, the solution is replacement of the chain and/or freewheel.
There are some other possible problems, but given the age, these are the most common.