When designing a new logo for the company such as Facebook What do you think about to know how to design it?

There are certain tins you should think about, as previously mentioned above Knowing your target audience is very essential but you should also do a research to know who are the competitors of your client what is the position of your logo between other brands.
Let your LOGO always tell a story which shows that the brand you designed the logo for is very solid then when you have all of these together it will help you choose your colors.

I think about target audience...
colors...
shapes...
typography...
competition...

I'd say I'd think of a philosophical concept that links the service or the product we provide with a chosen symbol meaningfully, to grab the customer's attention and make them think what's behind it and it shouldn't be so hard to figure out.
Also you use the initials of your company in a way.
For example see the ( Gmail ) logo, they used the letter M and the envelope symbol together to express the function.
Also sometimes the Airways companies add the crown over the major word/name to express the luxury and comfort , when the crown is added on the name of a restaurant for example it expresses the fineness of the service and food and the whole setting.
you must also choose the colors accurately,2 colors at most and use the art of making what's important must be prominent using color and size.

I think logo must be clear and according to company name and nature.

First, you need to think and write down some words that describe your company (taking your example: Facebook- communicating, friends, news,etc).
Then you find simple pictures representing that specific word.
That leaves you with a collage of pictures that you use to make several different sketches for your logo.
After you are done, you pick the best or your favorite logo.
Take your sketch, and start to lay it out.Start with the background, and then move forward, that way you have an excellent feel for the larger details of the logo.
Get to a point where you like the look of the logo.
Once you have the initial mockup done, step away from the logo and go away for a while.(The idea here is to start-up the logo again after your brain has had time to forget it a bit ).
Take a look at the logo.
What’s missing from it? How are you failing to visualize the elements the client wanted to present? Is there any way you can improve the condition of the design? If so, do your best to implement these changes.
Good luck .

Everyone has its own way.
My way is to concentrate the company (name and work of company).
Care about the colours and branding as well.

Creation of logo:create each aspect of mind such as Discipline,Kindness,Creation of mind, Passion toward progress,Thinking,Products,Strength,Information,Understanding.Belief,Display and Unity.
Most important colours will creats same as above.

It is possible to use the first letters actively own company

Right through the history you will see logos that sustained the time and are still shining are mostly the simplest ones such as Microsoft, apple, pixar, mcdonolds, KFC, and many many more to the list...as soon as we look at it or a part of it, we know its a part of particular brand etc..
A good Simple yet effective typography, unique font, shapes, symbolism, most of all while designing a logo for a big company think of how many places and sizes will it be used on, try re sizing it to a billboard and to a small tiny logo on a business card or a sticker..if it is playing ball...you've got a good logo.
Also you have to use colors according to the business that company is operating as if its a famous restaurant I ll prefer Yellow, Red over Blue and Gray's and vice versa if we are dealing with a corporate house...
there's a lot more to colors than just how it looks on the screen.
My advice, don't do anything complex but impactful and smart..
hope it helps

1st you have to speak with the company managers about the reasons why they wanted to change there logo for ...
maybe they like an extreme makeover for the logo, colors, shapes, brandings, and typography ..
you have to ask them way ...
to know what they expect form you ...
this is the answer for your question ...
then you can use the answer of (( Jasninder Jeet Singh )) and (( Rami Al Shaar )) as a guide lines helping you thru the process ..
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U should knw abt the history of da product then think abt a phalasophic concept or funcational thingy to present the product