Learn Dutch: Ik weiger te falen.

The verb weigeren (to refuse) is one of the specific verbs that requires te before the second verb in the sentence. It works just like English in this case: 'I refuse to fail' becomes Ik weiger te falen.

If I wanted to add a word like vandaag (today), where would it go?

It goes in the middle! You would say Ik weiger vandaag te falen. In Dutch, the te plus the infinitive verb usually gets pushed to the very end of the sentence or clause.

Why does falen only have one a, even though it sounds like a long vowel?

This is a great time for a quick open syllable refresher! When you split the word into syllables, it breaks as fa-len. Because that first syllable ends in a vowel, the vowel automatically makes a long sound. Writing faalen would be incorrect spelling.

Is weigeren a regular verb?

Yes, it is completely regular. The stem is weiger (which is why we use ik weiger here), and for 'he', 'she', or 'it' you just add a -t to make hij weigert.