"Can" and "could" are modal verbs.  English classes usually spend several lessons on modal verbs.

Can = to be able to do something.

"I can run five kilometres.  My brother can speak four languages."

Could =  a form of the modal can (multiple meanings)

- past -  "When I was young, I could run five kilometres" (past form of "I can run five kilometres.")

- future in the past - "Last summer, Tom said he could visit us in the fall, but unfortunately he got busy at work and didn't visit us." 

- conditional - "If I had more money, I could travel around the world."

- conditional of politeness - "Could you take me to the airport on Saturday, please?" (= Please take me ...)

Chris`s examples are all good. The indicative present tense form of should is can, which means to be able to (do something). The simple past of can is „was able to, or as Chris indicated could. Either one is okay. Or it can be in a future form, „when I was young I could run XYZ distance.“ And then it gets confusing because could also falls into the subjunctive case, the case of the unreal or hypothestical. An example would be „If she weren’t ill, she could (would be able to) come to the birthday party. And it can, of course, be used in the future, „if she weren’t ill, she could come to tomorrow`s party.“

The word has such varied uses I tend to use „to be able to“ as much as possible to distinguish them. But, you don’t have to. 

"Can" is ability now. It is what you are able to do, now. It is what you can do.

"Could" is a modal verb, and it comes from the word 'can'. "Could" has the idea of possibility, or doubt; that it is not certain. Could also talks about the past or future, where there is doubt, uncertainty, etc.

Eg. I can work on Saturday (can = able) , but I could not  work last weekend.

I can not work late tonight, (extra work, overtime), but I could if I had a  babysitter to care for the child.

I could cook you a delicious dinner if I had more ingredients. I can only cook you a simple dinner today.