Example JavaScript from the Working with GeoJSON tutorial at http://www.mapwolf.net/geojson

working_with_geojson.js

function addGeoJSON(geojson){
  // Create a GeoJSON parser that will convert our features 
  // to something OpenLayers understands.
  var geojson_format = new OpenLayers.Format.GeoJSON({
  	'internalProjection': new OpenLayers.Projection("EPSG:900913"),
  	'externalProjection': new OpenLayers.Projection("EPSG:4326")
  });

  // Create a vector layer that our features will sit on. 
  var vector_layer = new OpenLayers.Layer.Vector("Mountains"); 

  // Add it to our map so we can see it.
  map.addLayer(vector_layer);

  // Convert our GeoJSON to OpenLayers features.
  var openlayers_features = geojson_format.read(geojson);

  // Finally, put our features on the map by adding them to 
  // our vector layer.
  vector_layer.addFeatures(openlayers_features);
}

function init(){
    // Create a basic map using OpenStreetMap as the base layer.
    map = new OpenLayers.Map( 'map' );
    openstreetmap_layer = new OpenLayers.Layer.OSM( "Simple OSM Map");

    map.addLayer(openstreetmap_layer);

    // Lets centre the map around our point of interest. 
    // We also set the zoom level. 
    map.setCenter(
        new OpenLayers.LonLat(-9.7427, 51.9994).transform(
            new OpenLayers.Projection("EPSG:4326"),
            map.getProjectionObject()
        ), 15
    );  

    // Add our GeoJSON to the Map
    addGeoJSON(my_geojson);
}