There are various International agencies monitoring the ENSO conditions. El Nino declaration is based on the SST anomaly over the regions known as Nino regions and is located over the equatorial Pacific ocean as shown in the map.
(source: BOM, Australia)

Nino 1 : Latitude 0° to 5° S & Longitude 80° W to 90° W

Nino 2 : Latitude 5° S to 10° S & Longitude 80° W to 90° W

Nino 3 : Latitude 5°N to 5° S & Longitude 90° W to 150° W

Nino 3.4 : Latitude 5° N to 5° S & Longitude 120° W to 170° W

Nino 4 : Latitude 5°N to 5° S & Longitude 160° E to 150° W

As per NOAA of the U.S.

The Oceanic Nino Index:

The ONI is based on SST departures from average in the Niño 3.4 region, and is a principal measure for monitoring, assessing, and predicting ENSO. Defined as the three-month running-mean SST departures in the Niño 3.4 region. Departures are based on a set of further improved homogeneous historical SST analyses (Extended Reconstructed SST – ERSST.v5). Explanation about ERSST.v5 is given here. It is one index that helps to place current events into a historical perspective.

NOAA Operational Definitions for El Niño and La Niña

El Niño: characterized by a positive ONI greater than or equal to +0.5ºC. La Niña: characterized by a negative ONI less than or equal to -0.5ºC. By historical standards, to be classified as a full-fledged El Niño or La Niña episode, these thresholds must be exceeded for a period of at least 5 consecutive overlapping 3-month seasons.

CPC considers El Niño or La Niña conditions to occur when the monthly Niño3.4 OISST departures meet or exceed +/- 0.5ºC along with consistent atmospheric features. These anomalies must also be forecasted to persist for 3 consecutive months.

The other important agency monitoring the ENSO is the Australian Government – Bureau of Meteorology.

Bureau of Meteorology, Australia:

For declaration of an El Nino event any three of the following criteria need to be satisfied:

Sea surface temperature: Temperatures in the NINO3 or NINO3.4 regions of the Pacific Ocean are 0.8 °C warmer than average.

Winds: Trade winds have been weaker than average in the western or central equatorial Pacific Ocean during any three of the last four months.

SOI: The three-month average SOI is –7 or lower.

 Japan Meteorological Agency

JMA uses the SST anomaly of Nino.3 region for monitoring and declaring EL Nino or La Nina event.

JMA defines that the El Niño (La Niña) is such that the 5-month running mean SST deviation for NINO.3 continues +0.5ºC (-0.5ºC) or higher (lower) for six consecutive months or longer.