e.g. when we use wenn the verb goes to end. If the sentence starts with wenn, the second clause starts with verb as follows:
Wenn es morgen regnet, gehe ich ins Kino.
I think it is similar for weil and als too. But for denn, the verb doesn't go to the end, stays in second position. How can one know where to put verb for which conjunctions? What are the other conjunctions that follow this rule? Does second clause always start with verb?
"Weil" and "wenn" are conjunctions that introduce a subordinate clause; "denn" is a conjunction that introduces a main (non-subordinate) clause. Wikipedia list the following examples for these "coordinating" conjunctions: einerseits, anderseits, oder, entweder, sonst, aber, nur, außer, denn, selbst wenn, und, sondern, sowohl als auch, weder noch, indessen
Philipp is correct, the difference is between coordinating and subordinating conjunctions. On the second part of your question, any time a subordinate clause precedes the independent clause in a sentence, the independent clause's verb comes first. This is true when using subordinating conjunctions, but also things like infinitive phrases and the like.
For example:
Ins Kino zu gehen, habe ich gern.
The infinitive phrase "Ins Kino zu gehen" (to go to the movies), precedes the independent clause, "ich habe gern", so the verb has to come first in the independent clause. A bit of a clunky example, but I hope you get the idea.
Yes, the difference between coordinating and subordinating conjunctions is what lies behind the word order but it doesn't really answer the question because it's not always clear whether a clause is coordinating or subordinating. The examples of 'weil/denn' illustrate this well. I think in general it's easier to simply learn which conjunctions make a clause subordinate and which don't.
