Do you have any advice on finding match tickets and preparing to
attend a match as I plan a trip to Spain from the U.S.?
Unfortunately no. I mean, there's not really much to it other than what I said earlier: try to buy direct or at TI's offices and also stay tuned for when the tickets go on sale so you can purchase one. Note that certain teams (ie FCB) are not "companies" but a sort of "cooperatives" in which the ownership of the club is in the hands of the members, many of which purchase season tickets. The more relevant the game the fewer tickets available for non-members.
In any case, as mentioned earlier, the game will be announced a few weeks in advance and, while the final date might be moved, it's not the usual case.
As explained, when it's moved at the last minute it sometimes has to do with broadcasting interests by the media corporations. Many games of La Liga, especially those in which FCB or RM play, are broadcasted all over the world and the media giants pay ludicrous fortunes to broadcast it. This season's TV rights are managed by the Spanish company Telefónica (one of the biggest telecomms corporations in the world) which has paid 3.5 billion euros for it (yeah "b"illions!). When they see fit to move a game for business interests (ie a last-minute agreement with a broadcaster in the opposite side of the world, many time zones away) they "propose" it to the Liga Nacional de Fútbol Profesional (LFP) who organises the competition.
Contrary to what many might think, the most important match of the season is not necessarily the final of LaLiga (sort of your SuperBowl) -unless FCB or RM are contenders, of course- but the two games during the competition in which FCB and RM play each other. Last year, for example, each of those matches was broadcasted in over 180 countries around the world, with an estimated audience of over 700 million (http://www.marca.com/futbol/real-madrid/2017/12/23/5a3d6b4a22601d89168b45b7.html) so the game was played at 1pm instead of the normal evening schedule (national TV prime time).
Another very valid reason to have a fluid competition, as you mentioned, is indeed the fact that many of the biggest teams play several competitions at the same time. Thus, FCB for example, aside the LaLiga Spanish championship it regularly also plays the European Championship, La Copa del Rey, La Copa Catalunya and El Gamper... all within the same season.
For comparison, the SuperBowl attracts around 100 million viewers. Just saying this so you understand the magnitude of these games and the reason why things are the way they are.
About FCB's stadium Camp Nou
As per "preparations", there's not much to it either... head towards the stadium (if it's FCB's) at least an hour in advance, use public transportation (best option: metro) or walk, make sure you understand which entrance you need to use (https://suport.fcbarcelona.com/hc/en-us/sections/202693869-Queries-about-getting-into-the-stadium) as the stadium has 99,786 seats :)
Note the stadium is family and child-friendly and the ambience is mostly peaceful, we Catalans are accused to be rather cold and introverted despite being Mediterraneans if compared to say the Spanish or the Italians, and that shows in the stadium. This is not to say there isn't shouting and passion but it might be different than in other stadiums, overall less "noisy" probably.
But when the match is relevant, the overall atmosphere is quite something. This, for example, is a match last season between FCB and Chelsea for the qualification of the European Championship and the stadium was packed. Note the flags, which depict the colours of FCB (red and blue) and the colours of the flag of FCB's homeland, Catalonia (red and yellow).
More details: https://www.telegraph.co.uk/travel/destinations/europe/spain/catalonia/barcelona/articles/Barcelona-at-the-Nou-Camp-a-guide/