A Karnaugh map (K-map) is a tool used for simplifying logic circuits. In order to complete the K-map, you need to know the requirements of your logic circuit. In other words, how many inputs will your circuit have and what is the desired output for each combination of inputs. First thing you need to do is create a truth table for your circuit. I'm assuming you already know how to do this, if not let me know and I can explain.
For example, let's say your design has three inputs and you want the output of your circuit to be logic '1' whenever bit 0 and bit 1 are high and bit 1 and bit 2 are high regardless of the remaining bit, and logic '0' for all other input combinations. Your truth table would look like this:
bit 2 | bit 1 | bit 0 | Q (output)
0.........0........0.........0
0.........0........1.........0
0.........1........0.........0
0.........1........1.........1
1.........0........0.........0
1.........0........1.........0
1.........1........0.........1
1.........1........1.........1
Now you can use a K-map to get the most simplified logic circuit that will realize this truth table. As I stated in my previous post, three inputs require a 2x4 K-map. Bit 2 = 'A', bit 1 = 'B', bit 0 = 'C', and your output (Q) = f (A,B,C). You should now be able to follow the wiki example and plug these values into your 3-variable K-map to get your simplified circuit. To help you out a bit more, the resultant logic circuit will consist of two 2-input AND gates and one 2-input OR gate. Let me know if you have further questions, and I will be glad to help you out more.