Corinth is 84 km away from Athens. You can travel there by bus or suburban train(9e one way, 14e return ticket) from Athens and then take a local bus or taxi for the sites but that will be stressy and maybe more expensive for you. There are local buses from Corinth to Ancient Corinth.
A better idea (if you don’t have a car) is to book an organised tour because it will be much easier and it will include some other interesting sites of the area and a guide that will explain many things of what you visit/see.
The Isthmus of Corinth is situated at the distance of 78 kilometers from Athens and 6 kilometers from Corinth.
All the buses are going to Peloponnesus by the Old motorway and make stops at the Canal (two times an hour; 1,5 hours in a way from Athens, 5,5 euro). You may be lack of time to watch the Canal during this short stop, but you may use the next bus to go on your way after you finish an excursion.
We went to Epidaurus by an excursion bus and it was waiting for us about half of an hour until we completed watching beautiful views over the Canal and its Bridges.