Can we use would without an if clause as below. How can it be right?
A) Would you help me to open the door?
B) Yes, of course
or it's full form is
If you had mind, Would you help me to open the door?
would is the simple past of will. We use the simple past to describe things that happened in the past:
We knew that it wouldn't be easy
We also use the simple past of will for backshifting of reported speech
He said that he would be busy tomorrow
For almost all verbs, the simple past can also be used as a subjunctive for hypothetical conditionals.
If you are broke, I will give you some money - real
If you were broke, I would give you some money - hypothetical
For modal verbs (can/could, shall/should, will/would), we also use it to make a request or suggestion more polite. To tell somebody to do something, you can use an imperative:
Help me to open the door.
You can phrase this slightly more politely by saying
Will you help me to open the door?
To make that very polite, you use the simple past of will:
Would you help me to open the door?
Here are some more examples from this definition of would:
Would you mind sharing a room?
Would you like me to come with you?
Would you like some cake?
It is possible to use would in a conditional sentence (see the appropriate section of the link above) but this is a different meaning to making a polite request.
What would you do if you lost your job?
If I'd had time, I would have gone to see Graham.
Note that there are several other meanings of would.