What is your own philosophy of critical thinking?

Being clear about three items (two sets of definitions and a dynamic) is useful:

1.  "Critical" may mean censorious, bigoted; critical may indicate a key ingredient or factor.  From these two arise a) the failure of so-called "critical thinking" insofar as censoring, bigoted, close-minded, egotistical, and authoritarianism are incorrectly justified by the cliche "critical thinking," and b) epistemological clarity and continuing refinement of perceptions, upon which various logics may be developed and applied, towards the goals of parsing, solving, and re-solving various interests and concerns.

2.  "Thinking" arises of PIE *tong-, to think, to feel; OE pencan (the "p" is pronounced as "th") retains this unity as "cause to appear to oneself," including processes of imagination, meditation, consideration (Aristotelian observation of natural processes, including human processes) re-membering, ideation (Kantian, Whiteheadian, and neurophysiological archetectonics of ontological and epistemological processes), and desiring (of which "giving 'thanks'" is the English cognate).  Whitehead's "Adventures of Ideas," Husserl's "Ideas," and Heidegger's "What Is Called Thinking" are basic primers which help to clarify errors of reductive "positivism" (ironic tell re fallacy of "no values save value of no values") in e.g. logical positivism, etc., as well as naive subjectivism.

3.  The two multifold ingredients may be more or less diversified, and so it is well to be aware that a monotonic intoning of "use critical thinking" or "my critical thinking can beat up your less-critical thinking" typically becomes a caricatured catch-phrase, a parody of what e.g. Husserl, Heidegger, Whitehead, and Godel set forth. 

p.s.  "Update" answer:  Some of the more basic lessons learned:  the dogmatism of a process is reflected proportionately with its tendency towards Capitalization; the vain repetition of a slogan becomes a magical spell in proportion to the lack of awareness of the user as to the real processes at work (in maths, such ignorance of genuine categories of function ~ = blithe bijecting qua assuming incident structure--commonly noted as "for the person with a hammer (as their single process/tool), every problem (per pencan :-) 'appears to self' to be a nail"); and, when such category fallacies become -isms, e.g. objectivism, positivism, existentialism, humanism, and subjectivism, then fallacies re basic ontology, epistemology, and sensibility have reduced the -ism and its practitioners to at best incomplete/partial truths, typically taken as the whole/best truth. 

My own philosophy of critical thinking should be well known here,
I spent more than 10 years explaining it with dozens of examples or more.
Thousands of words to... a few said in haste but the majority explaining
the art and practise of modern critical thinking. It is nothing like the naive
turgid pap that usually goes by the name "philosophy", for "critical thinking"
is more than just a way to explain "philosophy"... and most if not all the
problems people have of explaining it are because they actually DO
Think that NOTHING NEW Hardly results from using the critical
method as the prime method of doing or writing philosophy (of course
explaining it too but as I said I spent nearly all of my time doing that
so won't be it again here.
How do I know how to do philosophy using the Critical method?
Again I have explained that MORE than once in saying that I was and
still am a student of the History of Ideas where we dissected this
question and were free to criticise it as our personal knowledge and
intuition allowed. And as I have said more that once it was a fabulous
environment in which to learn and which I did just that... learning and
honing my own meagre skills and of course learning just how POOR
and environmental-unfriendly was the antithesis of the taught objective
critical rational method of philosophy (the type of philosophy which
probably started well before Socrates but was akin to his critical
"mieutic method", that part of philosophy like I am doing now when
"thinking on my feet" and NOT Writing Something Down Which I was
Told or just Taught to write down.
The antithesis method of NOT USING THE CRITICAL Method of
philosophy is of course the much easier and lax method called The
subjective method (of philosophy).

I think people here even now in the much-vaunted & hope-filled 21st
century write their own timid and frankly stunted versions of "the subjective
method of philosophy" where they occasionally profess to be critical
but in fact are just (being) writing from the standpoint of "me" knowing
"what I know" in a world which carries on from there.. as if this
specialist knowledge is some sort-of-secret-kept-between only
"subjectives" and in reality has HARDLY ANY FORCE OR ACTION
on anyone else - or hardly at all unless they did become some 
wordy historicist idol-of-a-past, a past which indeed philosophy was 
written but without the "critical bit".
Don't believe me, or don't believe it?

Again I have addressed this previously here but no one would think
so (so) again I am certainly NOT about to "mince my words".

Just to say for example that I have brought up quite a few times the
outrageous (ly critical) emergency case of the Swedish schoolgirl
Greta Thunberg whose simple (Emergency) philosophy was about
"looking again AT THE SCIENCE because pupils were (I mean are)
NOT BEING TAUGHT THE TRUTH IN SCHOOLS which of course
as any dumball here (or there) should know means that students
today are not-being-taught-the truth either.
(Because if they did then significant numbers of them would realise 
THAT CO2 is rising exponentially and THIS CO2 CANNOT JUST GO
ANYWHERE. 
It Stays in the bloody atmosphere and T.H,I.S. is the principle reason
that we all here should understand that we all here are under a real
and "existential threat").

But you would think that all this COULD & SHOULD be discussed here,
philosophically no?

Lol... well I even had one legit commentator here say about that..
(peter m..)... has A THING About Greta Thunberg (!)
Too right I did, and I still do ABOUT HER BLOODY excellent-but-shocking
CRITICAL methodic Philosophy ; however stark and underwhelming to 
some here, versed-as-they-profess to be in "the critical method of philosophy".

(And just in case you MIGHT think that the above is about environmental
science not philosophy I think the likes of Jordan Peterson and Noam
Chomsky would have some argument against that. And so I bloody
would too).
For it's true that If SCIENCE can pronounce on something... then Philosophy
is sure to be able to do so to (and thus it would then be an "official
part of philosophy" I suppose...)... yet again... even things like
science FICTION is a proper part of any Critical Method of Philosophy 
I hope that you can agree !?

Have a nice day.

I think it includes curiosity, an understanding of bias, investigates opposing views, is aware of motivations such as greed, ego etc. understands how culture and counter culture create a tone or narrative.  It has a healthy level of skepticism, is responsible in taking a stand.  
 
 

Philosophy isn't about personal beliefs, it's an attempt to find universal principles through the use of logic.  Well, that's formal philosophy, in English words often mean more than one thing and the word "philosophy" can mean different things to different people.  Critical thinking, just means thinking clearly and well, critically.  One has to be able to question one's own thoughts and not be so dug into a position that one can't change.  Bigotry is the enemy of critical thinking.