The school district follows a complicated recipe to assign different parts of the city to one of four 'Tiers.' We think we understand it from reverse engineering some publications that the district has released.  Please note that when you look up your tier, the tier is not one that we calculated but comes from a CPS publication.
If any of this in error, or you would like to contribute to it, please email us.
First, the school district divides up the city into about 800 areas called census tracts. These tracts are small areas that the U.S. Census Burea uses for reporting data that the Census only collects from a sample of households. The school district uses this sample data when they assign each tract a 'Socioeconomic Score'
The Census Bureau also reports that data for smaller areas, and we do not know if there is a reason why the school district chose census tracts instead of a smaller or larger area. On average a Chicago census tract is about twenty city blocks and has about three thousand people.
Four of the numbers that go into a tract's 'Socioeconomic Score' are simple and come directly from the Census.
The district also uses census data to create a fifth 'Education attainment score.'
From the Census, the district finds the percentage of people over the age of 25 who have one of five different levels of education:
The district then plugs these percentages into a formula to make an 'Educational Attainment Score.'
Education Score = 0.2*(% Less than HS Diploma) + 0.4*(% HS Diploma) + 0.6*(% Some College) + 0.8*(% Bachelors Degree) + 1.0*(% Advanced Degree)
This score could range from 0.2, if no one graduated from high school, to 1.0 if everyone has a graduate degree.
The first version of the tier system only used census data, but the district added school performance to a tract's 'Socioeconomic Score' for the 2011 Admissions process. 
The school performance variable is itself a complicated animal--a weighted average of schools' ISAT composite scores.
Let's start with explaining what an ISAT composite score is.
Chicago public elementary students take the Illinois Standard Achievement Test (ISAT) every spring from third to eighth grade. Every year, the students are tested in reading and math, and in grade four and seven they are also tested in science.
To make the ISAT composite score, CPS looks at all reading, math, and science tests, and calculates the percent of these tests where a student met or exceeded Illinois's learning targets. So a score of 77% would mean that 77% of the scores on tests in reading, math, and science met or exceeded the state standards.
For student living in a given tract, CPS knows what schools the students go to. To get a school performance variable for a tract, they average the schools' ISAT composite scores, weighted by the fraction of students attending each school.
So, let's say there were 300 elementary students in a given tract, and they all went to one of two schools. A hundred of the students went to a school with a composite ISAT score of 75 and 200 students went to a school with a composite score of 60. The weighted composite score would be 65
School Performance Variable = (100/300)*75 + (200/300)*60 = 65
See Refinements to 2011-2012 Selective Enrollment and Magnet School Admission Policy for more detals.
So now the district has six numbers for each tract:
Next, the district calculates the tracts percentile for each of these numbers. For example, that means that it ranks all the tracts by median family income. Then, for each tract, the district calculates how many tracts have smaller median family incomes. If a tract is the 75% percentile for median family income, that means that 75% of tracts have smaller median family incomes.
The district calculates the percentiles for all six numbers separately, and then adds up these percentiles up to give each tract a 'Socioeconomic score'.
Socioeconomic Score = Percentile Median Income + Percentile Home Ownership + Percentile Education Score + Percentile Single-Parent Family + Percentile Non-English Speaking + Percentile School Performance Variable
For single-parent families, the percentile is the percentage of tracts with a larger proportion of single-parent households. The non-English speaking households percentile is also the percentage of tracts with a larger proportion of non-English speaking households.
Once the district has given a 'Socioeconomic Score' to each tract, the tracts are sorted from lowest to high. Going from low score to high, the district puts tracts into Tier 1 until 25% of the city's school age children are in tier 1 (from the census, the district knows how many school age kids are in each tract). Once 25% of kids are in Tier 1, then the district adds tracts in order of socioeconomic score to Tier 2 until 25% of kids are in Tier 2. The same happens for Tiers 3 and 4. At the end, there should be about the same number of school age children living in each of the four tiers.
Tier publications that the district has released:
In 2010, the Blue Ribbon Commission evaluated the system and found that fewer black students were being accepted. The commission recommended that a measure of school performance be added to the tier system. In addition, they also recommended that 70% of seats be allocated by tier instead of the original 60%.