Bitwise operations tend to be confusing because it uses some of the more cryptic symbols on the keyboard and what they do is less clear.

Code:

& - AND

| - inclusive OR (This is a pipe, SHIFT-\)

^ - exclusive OR (XOR)

~ - one's complement

<< - left shift

>> - right shift

AND:

Usage:

x = x & 0177;

This will set every bit above the bottom 7 to 0, then save the lower 7 to their original state.

INCLUSIVE OR:

Usage:

x = x | 0177;

This will set the bottom 7 bits to 1, and retain the rest from x.

EXCLUSIVE OR (XOR):

Note the difference from inclusive OR by its behavior with two 1 inputs.

Usage:

x = x ^ 0177;

This will reverse the bottom 7 bits of x. 

The advantage of ^ versus | is that you can get the original input again by XORing with the same number.

x == ( (x ^ 0177) ^ 0177)

This property means that XOR is used extensively in encryption applications.

ONE'S COMPLIMENT:

This is like XOR, but with only one number.  It reverses every bit, so 0110 would become 1001.

Usage:

x = ~077;

This will set every bit in x to 1 except the bottom 6.  This is an advantage because it doesn't matter what the word size of x is.

x = 0177700; Assumes x is a 16 bit value, if x is changed to a 32 or 64 bit value, you would have to go through and change every piece of code making assumptions about word size.

LEFT AND RIGHT SHIFT:

These two commands are probably the one's I use the most of any on this page.  They shift the bits either left or right by the number given to it, then usually fills the rest with 0s.

Usage:

x = x<<2;

This would be equivalent to multiplying x by 4.

Note:

When you're right shifting an unsigned interger, the empty bits will be filled with 0s.  When you're right shifting a signed interger, the results are less predictable and, depending on the machine, will either fill it with 0s or 1s.

Sources:

The C Programming Language 2nd Ed., Kernighan & Ritchie, pg. 48-49.