If you have brake fluid coming out of the drum, then the brake cylinder on that side of the car is shot and will need to be changed. If one side is shot then the other side can't be far behind, so the best thing would be to change both sides at the same time. The rear brake lining will also be completely drenched in fluid and will need to be changed too. At a minimum you will need to change the brake shoe on that side and the brake cylinder on that side. Brake shoes should be changed in pairs, so you should do both shoes at the same time. You should also have the drums turned, or buy new drums when you put new shoes on it. I have no idea how much you want to spend on the car, but on these old girls, the best bet is to do a complete rebuild of the rear brakes. Again, you can do the minimum and just do that sides brake cylinder and brake shoe and get the car back on the road for maybe $40, or you can do both side cylinders, shoes and turn the drums or buy new drums for maybe $50, or go all out and get everything and completely rebuild the rear brakes for about $120 with new drums. This assumes you will do all the labor. All you should need to do a complete rebuild is here:
1- brake shoes: under $20 at rock auto
2- new drums: AC Delco Professional under $23 each rock auto
3- wheel cylinders: under $10 each at rock auto
4- drum brake hardware kit: under $6 at rock auto
5- drum brake self adjuster kit: under $6 at rock auto
For how little the parts are you might as well change everything and do it once and forget about it for the foreseeable future.
One thing to note is that most of these cars use 2 left side wheel cylinders. So, if you buy one left and one right, the right one will not work.
If you are doing the rear brakes you should get the tools, Under $15 at you local Harbor Freight:
https://www.harborfreight.com/drum-...GD5w6xQlM5BMTAWZZusObfeE2-P_dkmUaAmauEALw_wcB
Really good video on how to do your rear brakes: