Lots of websites provide color palletes or themes, like Adobe Kuler.
But what if I have a specific color from a logo I want to use, and want to know what other colors go well with it? Is there any website that can help with this situation?
There are theories and studies how certain colors compliment each other and create a harmony for example using the color wheel.
If you do want someone/something to suggest you a complimentary color I suggest to look at the Color Scheme Designer.
But at the end of the day it's totally up you. There are renown designers and designs on the web using color combinations that go against all color theories yet they look great if not awesome.
how to use a specific color : you will love it.
which color will go well : do you really need suggestions? I don't think so.
You can use Photoshop or GIMP. There are also more specific utilities, such as Hex Color Finder and Color Picker Online.
In Photoshop, open the image (File -> Open) and select the Eye Dropper tool (shortcut: I). With the Eye Dropper selected, click on the area where you want the color code of. You will notice, in the bottom left the color has changed in the "Set Forground Color" area. Click on the color and a dialog will be displayed, giving you detailed information about the current color. You're probably interested in the HTML notation, which is identified as the "#" with a textbox next to it.
In GIMP, open the image (File -> Open) and again select the color picker tool (shortcut: O). Then click on the area of the image where you want the color of. Once you have done so, at the middle of the toolbox the color will have changed. Click on the color's thumbnail and again, it will give you a list of detailed information about the color you have selected.
Hope it helps,