It depends on the verb. Some verbs are separable, some aren't. There's no pattern, I'm afraid. A quick Google search led me to this list. Learner's dictionaries, such as Oxford and Cambridge, often give a few example sentences after each definition, which might help you figure out if the verb is separable or not.
One thing you need to remember is that if the object of the verb is a pronoun, and the verb is separable, you have to separate it.
Please turn the TV off.
Please turn off the TV.
Please turn it off.
* Please turn off it.
I'm bringing my children up to be polite.
I'm bringing up my children to be polite.
I'm bringing them up to be polite.
* I'm bringing up them to be polite.
If the verb is non-separable, this rule doesn't apply.
I'll look after your dog.
I'll look after him.
* I'll look him after.
An asterisk (*) before an example sentence means that it's ungrammatical.