With a center point at Madison and State Chicago is a well-planned city that is difficult to get turned around in, once you know the grid system.
In accordance with the Land Ordinance of 1785 a grid was mapped over the land of Chicago. The Ordinance specified for the land to be divided into townships, six miles square. Square mile sections of the townships were then numbered creating a grid that can help determine clear title for real estate sales.
As the city grew and combined with suburbs the numbering system became confusing. Multiple streets had the same name and the combined townships had repetitive numbers. In 1909 the city accepted a plan by Edward P. Brennan which unified the street numbering system naming the intersection of State and Madison as zero and numbering the blocks accordingly in each direction.
Now it is much easier to find your way without a map in the city of Chicago. From the center of the city (State and Madison) the blocks are numbered in each direction, there are usually eight blocks to a mile. Each block starts the next multiple of 100. For example one block may be from address 100 to 200. Each mile is marked by a major road, therefore 800 W (Halsted Street) is one mile west of State Street. Address numbers are even on the west and north side of any street and they are odd on the east and south side of any street.
For example if you are at the Newberry Library at 60 W Walton (north side of the street) and you want to go to the Art Institute at 111 S Michigan you will need to walk south east. At 200 East, Michigan is two blocks east of State. From 60 west the address numbers will lower as you approach State and when you cross to the east side of State the numbers will count higher. When you arrive on Michigan you will see that the street sign says N Michigan, letting you know that you need to walk south to find 111 S Michigan (east side of the street), about a block south of Madison.
There are a number of diagonal streets in Chicago which can make this trick a little more confusing, however it is usually obvious if you are on one of those streets, so you can easily get your bearings by stepping over to a cross street and checking the address. When in doubt Chicagoans are very friendly in providing directions.