As a summary of the above, we can say that infinitives can be connected to the main verb with different prepositions or no preposition. Which one to use, you just need to learn with the verb. The recommendation of the author is to learn a full phrase with verb, prepostition, infinitive and maybe an object. With the ready-made structure it will be easier to create new, own sentences.
Further it is important to remember that an infinitive construction is possible only, if the two actions have the same subject or, there is an object that functions as subject for the infinitive.
If there are more than one subject or, if there is an object the subordinate clause with the conjunction that works also very well.
However, if you feel it is too much for just one lesson. Just take your time. We have alreaddy suggested to always study the verb with the preposition and the object, one at a time and soon enough you will automatically find the correct option.