Learn Dutch: Ik wil een fiets zoals deze. - I want a bicycle like this one.

Zoals specifically means "like" in the sense of "similar to" or "such as". While als is used for direct comparisons of equality (like even groot als meaning "as big as"), zoals is used to give an example or show a resemblance.

Why do we use deze for "this one" instead of dit?

We use deze because it refers back to fiets, which is a de word (de fiets). If you were talking about a het word, like het boek (the book), you would use dit, as in een boek zoals dit (a book like this one).

Where is the word for "one" in the Dutch sentence?

In English, we say "this one" because just saying "this" often sounds incomplete. In Dutch, you do not need to add a translation for "one". The pointing word deze works perfectly on its own to mean "this one".

How would I change this sentence to say "I want a bicycle like THAT one"?

You would use die, which is the word for "that" when referring to de words. The phrase at the end of the sentence would simply become zoals die.