I've been reading that's it not good to use a lot of adverbs. I was told that cutting them out (which I am working on) will lead to stronger writing. How do you know when you're overusing adverbs?
This is a common generalization, yes, and one brought up very often here (not sure why). Adverbs aren't "bad" they're a component of language and communication. The idea behind the sentiment conveyed to you is this: adverbs are often used by inexperienced writers instead of using strong verbs that convey the same idea, or sometimes an even clearer idea, to begin with. Adverbs used as a crutch that weakens images is generally bad technique.
For instance (not going to be a great example):
1.) The man ran quickly, arms waving wildly, to catch the bus.
2.) The man tore across the sidewalk, arms flailing, to catch the bus.
2 uses fewer words and not only conveys the same thing, but the actions conveyed are stronger. "Tore" and "flailing" bring the moment to life, whereas "ran" and "waving" are weaker verbs, and the writing tries to cover it up by crutching the words with adverbs.
The second question I had was about dialogue tags. I heard that one shouldn't use words other than said as dialouge tags. Is that true or not? If so, what is wrong with using words beside said when a character says something?
One last thing: I feel like I am using 'said' too much in my current work. How can I cut back on that without people getting confused with who is talking?
There are also a ton of threads on this subject, but no, essentially what you've been told is not true.
The idea behind this supposed-rule is that, again, colorful tags used in an amateur way often cover up weaknesses in a scene. It's basically the show/tell thing, but specifically for dialogue. "Said" is "invisible," meaning you use it when needed for clarifying who is speaking and use nothing when it is not necessary (the start of a new paragraph or manner of speaking are often enough to show who is talking). Of course "screamed" or "whispered" or "asked" fall under the same umbrella. They're words the reader mostly breezes past because the dialogue carries itself--they're clarifying without being intrusive on the action of the scene.
Basically, the tags shouldn't explain the emotions of the scene, the scene should be making the reader feel those emotions. Tags or other "showing" devices aren't a good substitute for strong writing. If your scene is strong, you can use tags or "showing" for whatever purpose you deem integral.
If you search, like I said, though, you'll find a ton of these threads and much useful advice.