How can I find the cleanout for my cast iron drain line?
You basically have three main options for a cleanout:


Roof.  Most home during that era, especially with cast iron have a full clean out on the roof vent.
Main stack on lowest level.  This would be basements in some homes but guessing you don't have one.  Without a basement these can be on the first level or crawl space, usually first level.  If there is a cleanout opening it should have an access panel which could be any sort of panel size and less than 1' by 1'.  I would look in the center of the house or close to bathrooms/kitchen, really close to toilets.
Closer to the street, probably on you front lawn.  You should see a small manhole or some other sort of contraption for a cleanout to your street sewer system.  


Things to think about...


You need something to snake this.  Snaking old cast iron is not easy.  As it corrodes it becomes smaller inside.  You shaking metal inside that always isn't a good scenario.  Pieces break off and make a bigger mess.  So make sure you are using the proper tool.  We have no idea how big your yard is but in mine I need a 300 foot auger out ever two years to get tree roots.  I of course don't own one so I call someone.
Calling a plumber is not going to help you if you just want it temporarily fixed and snaked.  There are other companies that will do this for you local for $75 or so.  There are a ton in my area that for $50-75 will send someone out and let them snake for an hour for that amount - or until issue is fixed.  Calling a plumber could run you 4x the costs.
Which brings me to the real answer...  Just have a plumber convert your lines to PVC.  Most of the time this is a one day job and ranges in price from $750-1500.  I know you are trying to save money but having a plumber troubleshoot one time could be $300-400, and he very well may never touch the root cause of the issue.  Something like this isn't worth half-assing because it isn't something that is just broke but it is broke and getting worse.