What ways can tengo be used?
In what ways can tengo be used For example: Tengo que mejorar - I need to improve, the I need not I have or Tengo que dar - I must give, I must instead of I have. It just seems as tengo is used a lot more than just I have or I am.
3 Answers
This is an interesting question! I'm a native Spanish speaker and if you asked me, I would have never said that "tener" can mean "to be" in any context.
I guess we have expressions and phrases that sound weird for English speakers because they wouldn't use the same verb.
In Spanish, when we say our age, we say: "Tengo 20 años" and we are literally saying "I have 20 years old" in fact it is common for Spanish speakers beggining to learn English to say "I have 20 years old"
Maybe it is a weird concept because you are not used to it.
Tengo frío means I'm cold in English. If it sounds too strange for you, you can think about it this: I have the feeling of being cold.
You can use that logic with other phrases, such as I'm hungry. Tengo hambre = I have the feeling of being hungry.
But this doesn't apply to all the phrases that there are in Spanish with the verb "tener", so you may want to try to memorize them. The more you use them, the faster you will remember them.
If it makes you feel any better, English learners have to learn phrasal verbs that make absolutely no sense, that is not fun at all! 
By the way, I would have translated "Tengo que mejorar" as "I have to improve".
Tengo que dar = I have to give. Debo que dar = I must give.
Tener is always, at least in my mind, to have. I have hunger, I have 20 years of age, I have cold, etc.
The hardest one for me is tener razón = to have reason = to be right (in English).
This is something you can easily look up. I remember having a test in class with about 30 phrases.
Here are some:
You can also look up word reference and check this site.
However, there are probably a lot more useful things to memorise at this stage. Learn if you find a pattern eg hunger, thirst etc but a long list won't help
