The Spitzer-COSMOS survey (S-COSMOS) is a Legacy program (Cycles 2+3) designed to carry out a uniform deep survey of the full 2 sq deg COSMOS field in all seven Spitzer bands (3.6, 4.5, 5.6, 8.0, 24.0, 70.0, 160.0 u). This paper describes the survey parameters, mapping strategy, data reduction procedures, achieved sensitivities to date, and the complete data set for future reference. We show that the observed infrared backgrounds in the S-COSMOS field are within 10% of the predicted background levels. The fluctuations in the background at 24u have been measured and do not show any significant contribution from cirrus, as expected. In addition, we report on the number of asteroid detections in the low galactic latitude COSMOS field. We use the Cycle 2 S-COSMOS data to determine preliminary number counts, and compare our results with those from previous Spitzer Legacy surveys (e.g. SWIRE, GOODS). The results from this first analysis confirm that the S-COSMOS survey will have sufficient sensitivity with IRAC to detect ~ L* disks and spheroids out to z ~ 3, and with MIPS to detect ultraluminous starbursts and AGN out to z ~3 at 24u and out to z ~1.5-2 at 70u and 160u.