Working in the field helps us to learn how to apply theories to solve real-world problems, to apply […], and to […].
Are the "to" after each comma necessary?
As was suggested by Wudang, the parallel structure of the phrases helps draw them together. Often parallel sections of a sentence are introduced by a single word in the main part of the sentence, but in this case repeating the common word certainly makes it easier to follow. I assume that your intent was to have parallel sections as this:
The only problem is that you have the word 'to' in other places that might make it difficult to separate out which are part of the parallel structure and which are not, as this:
The first one obviously doesn't fit the pattern (as is), but the rest seem as though they could be parallel. If your intent is to focus only on those last three (and any additional ones), then you might reword the beginning to avoid the wordiness as:
In this case each of the parallel phrases correctly completes the introductory phrase, and the repeated word 'to' pulls the reader through, allowing a pause just before each section.
The alternate method would be to use the connecting word once as:
Either way works, so it would be just a matter of personal preference. May I suggest you check what Grammar Girl has to say about it? http://grammar.quickanddirtytips.com/false-series-parallel-construction.aspx
They are not necessary; you can write the sentence without them.
It similar to what I would write the following sentence: