A tip or gratuity is the amount of money a customer at a restaurant pays to the server in addition to the cost of the meal.

The server (waiter or waitress) is responsible for taking the order, delivering the order to the cook, and then bringing the food back to the table for the customer to enjoy.

 The general rule is that a tip should be approximately 15% of the cost of the meal. 

Obviously, the amount of the tip will vary depending on the quality of the service.  In other words, if the server is rude, forgetful, or disrespectful to the customer then the tip could very well be less than 15%. 
On the other hand, if the server does a terrific job, and does it with a smile and a pleasant attitude, then it is very possible that the tip could be more than 15%. 
It really is totally up to the customer to decide what amount to "tip".

In any case, since most restaurant workers depend on the money earned from tips as an important part of their total wages, it is just as important to understand how to calculate a tip (or gratuity) accurately.
 

Now, the first thing to realize is that since most of these calculations are made without the aid of a calculator (after all, how many people actually carry a calculator with them when they are going out for dinner?), it is important to be able to estimate.

So before we go any further let's practice estimating...
Most people estimate by using the next nearest whole dollar amount.
For example:
$43.68 ≈ $44
$16.45 ≈ $17
(note we rounded up to the next whole dollar amount)
$69.83 ≈ $70
Sometimes people make it even easier by rounding off to the nearest $10.
For example:
$47.18 ≈ $50
$28.19 ≈ $30
It really depends on how good the service was...but in any case being "good with numbers" is a real asset even at a restaurant.
 

Let's look at some examples:

John took his family to dinner and the bill came to $59.15
The waitress had been very pleasant and had done a very nice job getting all the orders to the correct customer. 
He decided that 15% would be a fair gratuity.
The first thing he did was estimate the cost of the meal at $60.  Then in his head he multiplied (60) by (.15) (15% as a decimal).
He arrived at "9" as an answer and so he knew that if he wanted to leave a 15% tip it would be an additional $9 added to the bill.
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Let's look at another...
This time it was a group of three friends who went out for lunch.  They decided that they would put their entire order on one bill, but that each would be responsible for their own amount.  Then they would split the tip.
Mary's order came to $14.50
Gina's order came to $13.75
Sara's order came to $14.25
That brought the entire bill to $42.50
The waiter had been extremely friendly and so they decided that a 20% tip would be a way of saying "thanks for doing such a great job".
Sara was the "mathematician" in the group so she was in charge of calculating what each person should pay.
She first "rounded" $42.50 to $43.
Next she multiplied (43) by (.20) and arrived at $8.60 for the tip amount. Split three ways she arrived at about $2.90 per person.  As is often the case, she told the other two that they each owed $3 in addition to their meal cost to cover the tip. That means that the final amount paid by each was as follows:
Mary: $14.50 + $3.00 = $17.50
Gina: $13.75 + $3.00 = $16.75
Sara: $14.25 + $3.00 = $17.25
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