The best way to get from city to city hands down. Train networks run like clockwork in Europe (for the most part) so plan a day in advance and show up to your platform. There are no TSA lines or security scanners at the station. Trains also provide you a better view of the country than flying.
Rail Pass vs Point to Point
Rail passes can be extremely useful however it all depends on where and when you're traveling. Scheduling 4 single tickets can actually be cheaper than a rail pass for 4 days. The longer the distance you're covering the more a rail pass makes sense. Also rail passes start to become more expensive the more countries you tack on to them. As a rule for myself, I generally don't do rail passes unless I'm traveling in country or multiple times between two countries.
For example, if I'm traveling from Paris to the Netherlands, to Germany and finally Austria, that's 4 countries but all relatively close together from each other. That brings the rail pass ticket to around $500. Where as if I priced out point to point tickets it would total around $200.
Purchase your ticket in advance for the longer routes. Saver prices will go from €79 to €19.
Time is money
Avoid wasting time on connecting trains by being proactive beforehand. Check the train schedule the day before you leave and pick a departure time that has the least amount of connections and allows you to arrive at your new city earlier in the day.
Make sure you're choosing the right train station. All large cities have multiple train stations around the city (Paris has six!). So once you book where you're staying, look for the closest station in that area. I made the mistake of just picking Paris as a train destination once and found myself on the opposite side of the city that I needed to be in. If I planned it right, I would have gotten a ticket that took me to Parid Nord which was 10 feet from my hostel. You can end up killing a whole day traveling between two cities just due to when the train leaves, how many connections you'll make, and any unforeseen delays.
Time is money and it pays to plan the trip down to the details as soon as you're done booking your flight. Once you have a good solid foundation of cities you'll be visiting and the trains you'll be on, then you can focus on either planning out the sights you'll be visiting. Just don't slack on the train schedules, it will save you hours of extra sight seeing time.
For example, check out of the hostel at 07:00 to make it to the train station by 07:15 allows me to save 1 hour and 30 minutes and 4 train changes when going from Paris to Amsterdam.
It sounds obvious but I try to leave early on travel days so I arrive at the new location earlier.