I designed my business card in illustrator (3.5" x 2"), my colors are CMYK process colors, someone told me I should separate the colors before sending it to the printer, is that right? or that is the print house problem not mine, so all in all does offset printing for a business card needs color separation ?
Everything which is offset printed requires color separations. That's simply how offset printing works.
However, color separations are the job of the print house. It is their area of expertise.
A designer should merely need to provide a valid PDF/X-1a file set up to the proper dimensions.
As always, if you are uncertain what your print provider will need... ask them! They are always willing to help with information.
I don't know why you're not doing this with a digital printer but...
Yes, you do need to separate the colors unless you want to pay for 4 colors when your job only has 2 or 3 colors.
Well, I stand by my answer but I will explain more.
You need to check if they do not mean to assign the colors as spot colors.
In Spanish, We have two clear distinct terms. Color separation and color selection, and they are not the same. See if they are not using the concept in a similar way.
If your logo is Red, a color selection will transform this color to some magenta and yellow and mix them together again when printing.
A color separation is when you assign your logo with pure red as spot color, for example, a Pantone Red 032 C.
Here are two examples, a "full-color" logo and one with only two colors.
In the first example, it is ok if the logo gets separated into CMYK components.
But in the second one, it is probably better to send the image as spot colors
Traditionally the process was totally different. For a color photography, you needed to screen it using 4 different filters. For a spot ink, you simply took the picture of the original.
Sometimes you used the exact same negative and "painted" in top of it, blocking some parts and leaving other parts visible. They were manually separated.
Now, of course, the process is different, and it is pretty obvious that the colors are "separated" when making the plates. But that part is just an automatic process. But what values you need to send to each plate, any plate, C, M, Y, K or a golden metallic ink, varnish or whatever, is a design decision.
Here is another example of how you can handle different plates for different projects.