T t, u;
vector<T> v; // declare a vector;
v.size();// is 0
v.push_back(t); // put t on end of v.  Other containers have push_front() also.
v.push_back(t); 
v.size();// is 2
v.resize(3);
v.size(); // is 3, entries are t, t, d, where d is the default value of T.
u = v[0]; // u is t
v[2] = u; // operator[] returns an lval.
v[3]; // is invalid, garbage or seg fault

optional info (but iterators are essential for other containers).

vector<T>::iterator p;  // pointer into vector
v.begin(); //iterator pointing to v[0].
v.end(); //iterator pointing to v[v.size()], an invalid location.
// standard use of iterator:
for (p = v.begin(); p != v.end(); ++p)
{ process *p }

w.resize(n, t); // if n > current size, fill in with t instead of default.

redundant, forgettable functions
int n; cin >> n;
vector<T> w(n); // equiv: vector<T> w; w.resize(n);
vector<T> w(n, t); // equiv: vector<T> w; w.resize(n, t);

w.clear() // equiv: w.resize(0)
w.empty() // equiv: w.size() == 0
w.front() // equiv w[0]
w.back() // equiv w[w.size()-1]


Key points.

vector indexing is zero based (like C++ arrays);
T [100] a;  a[0];
vector<T> v;  v[0];

Size can be determined (and re-determined) at runtime 
with v.resize(n). (unlike arrays)
Size can be incrementally grown with v.push_back(t) (very unlike arrays)

Performance is quite similar to arrays.
Conclusion: even when an array will do, always use a vector.