Q:

How to use 'tengo', 'tengo que', 'tener', 'tenerlo'?

I am learning Spanish following the Michel Thomas Method. It lists the following can be used for the verb "Have": 'tengo', 'tengo que', 'tener', 'tenerlo'.
How do I know when to use the right word?
As I understand it, it's probably like this:

Tengo = Have (e.g. Own)
Tengo que = Have to (e.g. Must)
Tener = to have (e.g. ? - How is this different from 'tengo'?)
Tenerlo = to have it (again, how is this different from 'lo tengo'?)

What's the best way to remember it/understand it?

A:

Tengo = I have (you could think of it as "I posses something" although the meaning is wider than that)

Tengo un tractor amarillo

Tengo que = I have to

Tengo que ir al médico
Tengo que terminar este informe para las 5

Both come from the verb tener (and here the conjugations). Realize that even if Have means "Tengo" (and has means "tiene") it can also mean "tenemos", "tenéis" and "tienen". And that could change with the verb tense, so "have" has a broader meaning than just "tengo" and "tener". I would stick to "Have means Tener".
"Tenerlo" and "lo tengo" are the same thing. You could favor one over the other for stylistic reasons in a given sentence, but the meaning is the same. The only difference between the two is the conjugation of the verb.

