Understanding the concept of the limits and fits is very important for a mechanical design engineer. This geometric dimensioning and Tolerancing (GD&T) tutorial will explain the concept with an example 
If you are designing a shaft and hole pair then you have to use the limits and fits. Typically the GD&T limits and fits of a shaft and hole pair are represented by a group of numbers and alphabets, like: 90H7g6. By specifying such sets of numbers and letters in the drawing, you will actually provide all the necessary information required for manufacturing the shaft and hole pair. 
But how to specify it? For specifying the limits and fits you decide the following three parameters:
 Basic Size: Decide what should be the basic size of the shaft hole pair. It is the dimension to which tolerance are specified.
For example, 90±0.5 has the base dimension of 90.
The base dimensions of both the shaft and the hole should be same.
 Fits: Decide what kind of fits you require for the shaft and hole pair. Is it clearance fit or interference fit? On the basis of this decision you will select the two alphabets (H and g of the previous example) of the limits and fits specification.



For specifying the hole you will use the capital letters from A to Z. And for specifying the shaft you will use the small letters from a to z.
If you require clearance fit, then use a capital alphabet between A to H (for specifying hole) and a small alphabet between a to h (for specifying the shaft).
If you require interference fit, then use a capital alphabet between H to Z (for specifying hole) and a small alphabet between h to z (for specifying the shaft).
For the hole base system, hole tolerance should be H and for the shaft base system the shaft tolerance must be h.
See the figure for better clarity: 

As you move from A to H (or a to h), the fundamental deviation will decrease, again if you move from H to Z (or h to z) the fundamental deviation will increase. So, select the shaft and hole tolerance symbols based upon your fundamental deviation requirements.
 Tolerance Grade: The numbers written after the each alphabet (7 and 6 for our previous example) signifies the tolerance grade. You can specify any number between 2 to 16. Lesser the numbers, tighter the tolerance zone. Tighter the tolerance zone, more precise machining operation is required. In other words lesser the tolerance grade costlier the machining process.
You have to use the ISO 2862 table (Hole and Shaft Tolerances) for finding out the maximum and the minimum tolerance value for a specified basic size and tolerance grade. How? See the next example. 
Say, you have to design a 20 mm diameter (basic size) shaft and hole pair of close running fit to be manufactured by reaming and turning process. Take hole base system.
Solution:
 For hole base system, the hole tolerance zone symbol must be H.
 For close running fit, the combination of Hf is good enough.
 For reaming and turning process, the tolerance grade should be 8 and 7 for the hole and shaft respectively.
 So, the final limits and fits specification becomes: 20H8f7.
 According to the ISO 2862 tables, for 20mm basic size the tolerance limits for the hole (H8) are: 0 and 0.033 and for the shaft (f7)are:  0.020 and 0.041. This is the cross check.

You have to apply the GD&T concept of the limits and fits for design of shaft and hole pair. While specifying the geometric dimensioning and Tolerancing limits and fits you should be aware about the machining process, allowable fundamental deviation, and kind of fits for the hole and shaft pair. 