Create a vector source

var vectorSource = new ol.source.Vector({});

Initiate Map Object and add vector Layer to the map and Source as the vectorSource

var map = new ol.Map({
  layers: [
      new ol.layer.Tile({
      source: new ol.source.OSM()
      }),
      new ol.layer.Vector({
          source: vectorSource
      })
  ],
  target: 'map',
  view: new ol.View({
    center: [45, 5],
    zoom:5
  })
});

Transform the projection from source projection system to target project system.

var points=[];
for (i = 0; i < 10; i++) { 
    var xx = Math.random() * (xmax - xmin) + xmin;
    var yy = Math.random() * (ymax - ymin) + ymin;
    points.push(ol.proj.transform([xx,yy],'EPSG:4326', 'EPSG:3857'));
}

pass points to the ol.geom.MultiLineString([]) constructor

var thing = new ol.geom.MultiLineString([points1]);

Create a feature and add geometry as a thing

var featurething = new ol.Feature({
    name: "Thing",
    geometry: thing,
    style : new ol.style.Style({
      stroke : new ol.style.Stroke({
        color : 'red'
      })
    })
});

Finally add it to source

vectorSource.addFeature( featurething );

Note : It is very important to put proper source and target projection systems