If you want to browse a different instance directly, you just type in that instances URL into your browsers search bar, though this is not how most people look at other instances.

In the upper right, you will likely see a magnifying glass icon for search. When you click on it, you will see a page like this:

The first box in the upper left that reads "All" (The one to the left of "Subscribed") let's you choose the type of result you want from your search. Using this box you can search for all, comments, posts, communities, users, or URL.

The selector to the right with the choices Subscribed, Local, All, Moderator View (if you moderate communities) allows you to scope the source of your search results. Subscribed will only show results from communities you subscribe to, local will only show results from your home server (lemm.ee in your case), All will show you results from everything lemm.ee federates to (such as lemmy.ml, lemmy.one, and many more), and moderator view will show results from communities you moderate.

If you set that first box to "Communities", set the selector to "all" and then search "asklemmy", it means you want to see communities from all federated instances that match your search. The result will also show how many users are subscribed to each.

This is what I see when I do this. As you might notice, there is more than one ask lemmy community, because each instance can have their own! If the result is not on my home server, you can see that it adds the name of the instance it is on (for example the first result is the asklemmy on my homeserver, but then the second result is the asklemmy on lemmy.world, so it shows this.

If you leave these settings the same, and enter in two spaces as your search term, it will return everything, and you can paginate through every federated community that you can go visit, subscribe to, and communicate through. Alternatively, you can click "Communities" at the top of the screen on your main page and change the selector there to see this.

As to your question about finding an instance that suits you, there are a few pages like https://join-lemmy.org/instances which will let you browse instances. Each instance typically has a description explaining what the purpose of the instance is. Some are geared towards hobbies, others are for general use, some are for specific locations, some are for ideological beliefs, etc. On your main page on lemm.ee, at the top, you will see that same selector for "Subscribed, Local, All, Moderator View". When you browse "Local", you will only see posts from other users on your own instance and it's communities. This is really great because you can actually come to get to know other people pretty well on your home instance. It's the same as being able to see what is going on in your own town, and have a smaller community of people interested in the same general theme, but then also being able to interact with every town in the world by browsing "All" instead.

Instance owners have the power to do a few things which are important to know. They can turn off new user account creation for their servers (because if they are paying for server space, it is a problem if suddenly you have 10,000 users on your instance creating content) so you can't necessarily create an account on any instance. If you hit join on one of them on that page though, it should let you know if they are open for new accounts when you go through the sign up process.

Instance owners can also defederate other instances. This is a feature for cases where, let's say you have someone create a lemmy instance which is there just to make a group of mean people, who go to other instances to be mean. If every other lemmy instance were to defederate them, they become like a single standalone website without federation. Their comments and posts, votes, etc do not show up for anyone except them, and their content can no longer be searched for or seen by those who don't federate with them.