What you want to do is make a collection of student objects.
In C++, the std::vector class is generally the best choice for a collection type, and in your case as well.
How to use a vector
To use an std::vector you must first #include the <vector> header file. Then you can declare an std::vector object with the following syntax:
std::vector<T> name;
where T is the type of elements you want to store in the vector, and name is a name for the collection. In your case, you want the type to be student, and a good name for a collection containing students would be students, for example:
std::vector<student> students;
Adding objects to the vector
Now you can start adding student object to the vector. The push_back() function of the vector class can be used for this, like this:
students.push_back(foo);
where foo is a student variable you have created earlier.
Accessing objects in the vector
Now that you have added a student to the vector, you can access it with the at function:
students.at(0);
The above line will access the first object in the vector. The at function is also really useful if you accidentally try to access an object that's not in the vector, for example, you try to access the second object, which we haven't added yet:
students.at(1);
Because we only have one student stored in the vector so far, trying to access the second student with at will result in an error. Which is great! Now we know we did something wrong, and the error message will probably even tell us what we did wrong.
About vector vs raw array
A raw array like int numbers[10] will not tell us if we accidentally try to access over the end of the array like int x = numbers[10]. There will be no useful error messages to tell us were doing something wrong, the program will probably just silently continue execution and start behaving oddly. Which is what we as programmers don't want. Thus a vector is a superior alternative.
Note that with a vector you also don't have to specify a size, as with raw arrays. vectors will automatically grow as you add new objects to it, so you don't have to worry about adding too many.