How do I in general realize a universal C-algebra generated by some generators and relation as concrete C-algebras? For example, I know that universal C*-algebra generated by a single unitary is $C(\mathbb{T})$ by functional calculas. I am looking at the following examples to work on:

1. universal C*-algebra generated by single self-adjoint element whose norm is 1.
2. universal C*-algebra generated by single positive element whose norm is 1.
3. universal C*-algebra generated by single normal element whose norm is 1.
4. universal C*-algebra generated by single projection.