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There are actually many factors that can lead to the rise of a new species:</h2>
Changes in the environment (this is a very general and non-specific way of speaking and you should probably not add this to your list) - the environment is under constant change, but the changes are only noticable after some years or decades (if the changes are drastical in months). These changes lead to changes in species, that also, if too drastical, can originate new ones.
If a species changes, wont it just be the same species with different characteristics? - No, because not all individuals will change. If there are the same species in India and in the USA, let's say, but only the ones in the USA change, there will be one species in India (original) and another in the USA with new characteristics (new species). Also, even if they're in the same geographic location, we cannot guarantee that all individuals wil change or will change the same way.
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Natural selection - the selection of best-adapted individuals can make new species out of the better adapted ones. All we need is a "base-species" where individuals have different characteristics, with no paricular function. Suddenly, things start to change and only the individuals with certain characteristics will survive originating a new species from the now extinct one.
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Isolation - when some individuals separate themselves (during migration, a hunt, or simply a separation) they can develop different traits depending on where they go and how they live.
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Genetic drift - to keep things simple, a genetic drift is when modifications in a gene occur (or eliminations of a gene occur), either because of death or because of a lack of reproduction within a species. This can clearly originate new species, since we're dealing with genes.
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Genetic mutation - genetic mutation is a process in which the DNA sequence of a species mutates (changes), through substitution, deletion or insertion. This is the main reason of diversity within species or genus.
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<em>Note: there are more types of genetic changes and isolations we could name (also some evolutive processes) but the above are the most important ones in my opinion.</em>
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Hope it helped,
BioTeacher101
