I'd like to point out, that my knowledge in biology comes almost entirely from high school, so I hope that my question can be answered without getting too technical.

 

As far as I understand mechanisms of sexual reproduction, it is dependent on chromosomes, which go by pair. Female reproductive cells have half of them and male the other half. However since there are examples of species that have different number of chromosomes and yet share a common ancestor, how does then the creation of a new chromosome work? I understand, that evolution is a long and continuous process, so you can't pinpoint the first member of a new species, but when it comes to something like the number of chromosomes, I don't understand how you can by gradation get from let's say 13 to 14 pairs and if it happens anruptly, then how does the first life form with a different number of chromosomes reproduce?

There are species with variables pairs of chromosomes within the species, so having a mismatching number is not necessarily always an obstacle to reproduction.

There are som examples on this page of new species created by polyploidy: http://www.talkorigins.org/faqs/faq-speciation.html