That is, keep in mind a few essential steps and elements, and you should be able to fly.  First, the basics of writing critical essays are the same for writers of most modes.  Here are the modes that you might directly or indirectly be asked to write in—might be assigned the steps for or told to write an X essay using:

ANALYTIC-A classic style used in art, science, history, psychology,
education, and most other disciplines across the curriculum to explore
and investigate an idea, process, person, action, or attitude.

ARGUMENTATIVE-Used in more advanced English classes, in
philosophy, and in courses which include theory.

COMPARATIVE/CONTRASTIVE-Used in most courses where specific
analysis of like and unlike elements, characters, and ideas lend
themselves to comparison.

DEFINITIONAL-Written when we apply a more thorough study to a
topic, especially an abstract one.

DESCRIPTIVE-Used to more intensively, more concretely cover an
idea, item, or subject.

EVALUATIVE-Often confused with analytical, the evaluative essay
moves beyond the what and how to the how much...we put a value on
the topic here.

EXPLANATORY-Also called the expository essay (though I tend to
see all essays as expository, as exposing a truth about something).  
With this type we further our own and our readers' understanding of
the subject.

PERSONAL-Also called the response essay, the personal style
essay is still well written (readable for an audience other than the
writer), but is more informal--containing narrative details that entertain.
RESEARCH-While most essay types will include references or will
quote authorities, the research essay is mostly informational, using
the findings--the stats and facts--we made investigating the findings
of others.  

Now critical essays may fit better in or work better as one of the above modes, but all essays at the college level are really “critical” in nature.  That is, if you look up critical in the dictionary or online, you will find that it does not necessarily mean negative or picky or bashing, but just means, from the Greek word, kritikus, “to discern”.

So what do you discern in critical essays?  A given topic or issue (which is a controversial topic with sides), which you incorporate into a thesis and supporting ideas and details.  Here is what you should have in a critical essay:

An engaging opener- hook, lure, interest your reader.  Use a story, a fact, an extended definition, a quote, or a direct address…where appropriate.  That is, use whatever fits best with the whole essay and whichever kind of into you are best at writing.

A thesis- here you state, or assert, your position.  This is the overall opinion that adds up all your points…which follow the thesis as support.

Support- here you include statistics, narrative/non-fiction examples, statistics, authoritative (and respectable) quotes, analogies (relevant and apt), and other elements that help to “prove” your position.  In the case of critical essays based on literature or other works of art, this will also include what is called textual evidence (passages from the work as you describe or directly or indirectly quote/cite them).  In an argumentative paper, this section will also likely include the opponent’s side, concessions, and refutations.

Good closure – whereas in some critical essays the closer is the thesis, in many assignments you are taught to leave the thesis at the front of the essay and wrap up your writing in the conclusion.  Don’t bring in new examples, but do leave the readers questioning their positions, challenged with ways to take action, or reminded of what your goal was to begin with.

The components of the critical essay, then, as they are in most modes and college coursework, are those that you would use later on, too, in your job or online, even!