If you are going to a match, there is a station called "Manchester United Football Ground" that you can get a direct train to - from Piccadilly, these trains leave from platform 14, which is not in the main station; you should use the bridge that is at the far end of the platforms from the station buildings to reach platform 14. Trains to this stop only run on match days, so if you're going for a visit, then you can't use this option, and your best option will be the tram.
Google Maps wasn't loaded with Greater Manchester public transport until 2014, which is why your Google search didn't help. If you do that search now, it will advise you to use a Metrolink (tram).
After arrival at Manchester Piccadilly railway station, walk to the end of the platforms and go through the barriers to get into the concourse. Then turn left and there is a lift and some elevators going down - these are signposted "Metrolink" and also "taxi" and lead to the tram stop, which is at a lower level than the main railway station.
For Old Trafford, you can board any tram headed for Altrincham, Eccles, MediaCity, St. Werburgh's Road, East Didsbury or Manchester Airport. From an Eccles or MediaCity service, you get off at Exchange Quay; from any other service, you get off at Old Trafford. Both stops are about five minutes walk from the football ground. Note that trams to Bury or Rochdale go in the wrong direction; do not board one of these.
From Exchange Quay, you need to use the bridge across the canal, and you should be able to see the ground once you're over the bridge.
From Old Trafford, walk past the cricket ground, which is on your left as you come off the tram, and you should be able to see the football ground.