Taking classical to mean "Haydn-Mozart-Beethoven," that's the time of the transition between musicians being servants working for the nobility and musicians becoming independent professionals and impresarios.

How hard was it for Classical Musicians to get noticed?

It was hard, it has always been hard.

First of all, they needed to work a lot on their skills. It's not like they just woke up one day being super good at playing and composing. Musicians and their families tried to find the best teachers (it was private instruction for everybody, this was not a thing you studied at a university), that some times involved traveling significant distances.

Some were born in families with a long musical tradition, and their relatives were their first teachers. Being able to study under a prestigious musician helped a lot. Not just because of what they were able to learn, but because of the pedigree (so to speak). For example, Haydn offered young Beethoven to indicate in his published music that he was a "pupil of Haydn" to help his career take off. Beethoven didn't like that idea (think of something along the lines of "I don't need an old man to tell people they should listen to my music").

In any case, they worked hard for YEARS. Some people think Mozart and Beethoven were just naturally good. Yes, they were unbelievably talented, but also worked very hard.

There was a lot of competition. See, there were only so many high paying jobs. Those positions would be found in the great cities, artists were following money and power... The nobles would want to get the best musicians for their court. It's not only about having nice music, but it was also a way to show their power and wealth. You wouldn't be a great noble, or a great ruler, if you lived in a tiny house where nothing happened. You would want magnificent buildings full of amazing art, and a great musical life.

Young (and not so young) musicians would go to the big cities trying to make a name for themselves. They would some times get an in because of their teachers, their families, their friends and so on, but they had to be good. The rich and powerful would some times try to steal the talent from other rich guys, and top notch musicians would get offered positions in their courts.

and also how DID they get noticed?

Musicians would want to be recognized because of their skills playing an instrument, the music they composed, and their ability to lead ensembles (the modern conductor didn't quite exist, but they were working with ensembles and kind of conducted concerti while playing the solo part).

What did they do to get recognized? Well, they would organize concerts. Some rich family would host a fancy concert, and later the musicians would organize the event themselves (investing their money, or getting somebody else to put the money and later get a part of the generated income).

It was serious business, with lots of competition. Here's a story of Beethoven dealing with a guy who was trying to get noticed by using Beethoven's music. And there is this other story of Beethoven p0wning this other guy.

Musicians would also publish their music, that helped them getting their music to be known in other places (particularly in other big cities). Wealthy people would commission works from the top and fashionable composers. It was great for both parts because the rich people would get nice music, and the musician would get paid AND would be able to later say the rich and wealthy are interested in their music. Musicians would send the music and get paid, and the patron would get the exclusivity rights for a period of time (a year or two). The composer would not publish the music during that period, and the rich folks would play themselves the work (yeah, some of them were actually competent and even good musicians) or get their musicians to play it exclusively. Think of one rich lady rubbing the news on this other rich lady she despises, the fact that she got this new super great piano sonata by the great and only Beethoven, and she can't have it!

Musicians would later get commissions from organizations. For example, Beethoven's glorious 9th symphony was commissioned by The Philharmonic Society of London in 1817.

It's similar this days. Are you frequently playing in the great concert venues of the big cities? Are you composing music for famous events, organizations, or patrons? Is your music being played all around the world / are people buying scores for your music? If you answered no, you are probably not at the top of the food chain. These days we add recordings to the list but, yeah, they didn't have those.

Did they have "managers" or people who shared their works across the world?

Kind of, once musicians became independent professionals. Before that happened, well doing musicians were pretty much servants employed by the nobility and had limitations on what they could do. They were not always paid a lot, in some cases they were badly paid... But even then the arrangement gave them something they wanted (stability, prestige, etc.)

Haydn’s two successful seasons in London (he was in Vienna before that) were handled by J. P. Salomon. He undertook the business arrangements and the risk, and also played the violin in the concerts.

There were several intermediaries dealing with the commission for Beethoven's 9th symphony.

Gaetano Belloni was Liszt's secretary in Paris, he made arrangements for his traveling and was kind of a press agent.

I think famous musicians started having managers/agents in the second half of the 19th century. This certainly had can impact in the economy of the music world during the 20th century.

Publishing houses would print music in different cities. Some times different companies would print the music in different cities, some times it would be the same one handling it. Printed music made musicians known in in distant places before the classical period.