Just to make it clear: that discount is only applicable for bus, tram and metro travel, not for trains.
The ICD is easy to avoid towards Utrecht, as there are no ICD services there.
Getting a train from Amsterdam to Utrecht is really easy, as IC services from Amsterdam Central (or Amstel) to Utrecht Central run every 10 minutes from Monday till Thursday and every 15 minutes from Friday till Sunday. Besides that, another option is the train from Amsterdam South or Amsterdam Bijlmer ArenA to Utrecht which runs every 15 minutes (with a few additional trains at peak hours).
Just be aware those trains have various destinations, IC-trains to Nijmegen, Venlo, Heerlen, Maastricht or Eindhoven all go towards Utrecht from Amsterdam. You should especially pay attention on the way back as from Utrecht there are trains towards Rotterdam that run via Amsterdam, but also a lot which take the direct route. (Although the platform used will already tell you which train is the right one: trains to Amsterdam in general leave from platform 5 or 7 in Utrecht; occasionally during engineering works 14 or 15 is also possible)
I don't now that much about the Amsterdam tram system, but the Utrecht one is fairly straight forward as it has only three routes: route 20 and 21 form the core service (both every 20 minutes) from Nieuwegein and IJsselstein through the southern part of Utrecht to Centraal Station Jaarbeurszijde, followed by a sort of rollercoaster (a winding tram track over a viaduct and then through a tunnel) to Centraal Station Centrumzijde. The latter is the terminus in the late evening and on weekends, during weekdays trams continue towards the Utrecht Science Park. Between Centraal Station Centrumzijde and Utrecht Science Park route 22 increases the frequency to 9 trams an hour (12 in the morning peak)
For Utrecht city, a day ticket is available for € 6,95 which is a bargain should you make more than one return trip:
https://www.u-ov.info/abonnementen-kaartjes/product-details/UFJPRFVDVF9UWVBFOjEyNQ/dagkaart-1-dag
For the trains between Amsterdam and Utrecht: using a contactless card you'll pay full fare (same fare as with an OV-chipcard). When booking in advance (at least one day) you might find a PrijsTijd Deal in the NS journey planner offering 20-60% discount, but e-tickets cannot be exchanged and you are required to travel within the specified timeslot.