I want to take a trip similar to that but I have never been out of the country. I don’t even know where/how to start planning something like that. What are the necessities to travel? What do you do at every city? The only trips I’ve really ever taken are for baseball stadiums & to the beach, so much different i think.
Where do you want to go? Pick your top destination first. It can be anywhere, but for your first time, you're probably best off picking a major tourist destination with lots of flights and good public transportation: London, Paris, and Rome are the easiest and biggest. Tier 2 includes places like Madrid, Barcelona, Munich, Vienna, and Amsterdam. I probably wouldn't go east of Budapest on my first time unless you're particularly brave and comfortable being lost, as those areas generally have worse public transportation and fewer English-speakers.
Once you have your main destination, scrub the area for secondary locations. Some loops or pairings are easy, like Rome/Florence, Paris/London/Brussels, or Vienna/Prague/Budapest. Others require a little more digging. Searching "day trips from [desired city]" can be an excellent way to turn up less-noteworthy sites that are still worth visiting. Take note of transportation and how you'll get from one place to another. Trains are very convenient in Europe, but taking a bus can be stressful, at least for me. There are also tour groups that will host you on a lot of these, but those come with their own trade-offs. If you're traveling between cities, make sure to think ahead on how you're getting home. This may be an unpopular opinion, but I like to have my more laborious flight going out there when I'm excited about the upcoming trip than coming home when I'm tired and deflated to be heading back to the real world.
Once you have an itinerary, start figuring out what you want to do in each city. There are plenty of websites out there if you search "X days in X city" that provide suggested itineraries. However, what I like to use best for a comprehensive guide is TripAdvisor. Pick out a number of sites that interest you, and then look up their location and group them into clusters that you can knock out together. Make sure to account for public transportation or however it is that you will get to that general area of the city. Also consider how aggressive you want your pace to be. I like to pack in full days, but it does get tiring, especially if you're in a hotter area (Italy, Spain) and it's the summer.
If there's a particular area that interests you, I've spent a lot of time researching and putting together loops (not complete itineraries) and am happy to share details from my trips. For your very first time in Europe, the easiest thing to do would be to go to London. It wasn't my favorite city, but you can get a direct flight from practically anywhere, it has easily-navigable public transportation, everyone speaks English, and there's plenty to do. Then, after a few days of getting your feet wet, you can take the train to Paris, which was one of my favorites, which is only a small step up in difficulty.