English has a melody and a rhythm. To sound like an American and be easily understood, you’ll need to learn the melody and rhythm of English. Also this melody and rhythm changes depending on the situation, for example a statement can be made into a question using intonation, and emotion is often expressed with intonation.
If you sing or play a musical instrument this will be easy for you. I also think it will be easy for speakers of Latin and Germanic languages. But having (supposedly) no musical ability isn’t a reason not to try learning the music of English; there are Americans who think they have no musical abilities, no sense of pitch or rhythm, and in fact they might not be able to carry a tune (sing on pitch); but they speak English with perfect intonation and rhythm. (Most Americans aren’t even aware of how musical spoken English is.)
The important thing to focus on is sentence stress; which words in a sentence or phrase get stressed. Stressed words are louder and higher in pitch.
As would be expected, the words that get stressed are the important words. These are the content words; if you remove a content word from a sentence, you’ll be missing something essential. Nouns, primary verbs, adverbs, adjectives, and negative words (can’t, wouldn’t, don’t) get stress. Think of stressed words as words that need to be heard clearly. Consider, for example, that at least nine out of ten times, numbers get stress. Also, stress is used when clarifying or specifying. For example: “Are the violets red?” “No, the roses are red.” The most stressed word in the second sentence is “roses.” Obviously, intonation can only be heard. But it’s important enough that when writing, bold and italic fonts are used on some words, in addition to emoticons, as ways to communicate what would normally be indicated by intonation.
In a sentence, words vary in stress. For example, consider this sentence: “As you know I flew with this man Striker during the war.” The words that are stressed the most are Striker and war; you, know, and flew also receive stress.
You can listen to that sentence here:
There are usually a couple different ways of saying the intonation of a phrase without a significant change in what is being expressed; so if you say something differently than how you hear a native speaker say it, your intonation might still be correct.
Listen to American speech, and copy it. First, ignore the words, and just say “la” for each syllable, like you’re singing. It might be easier to hear the melody in female voices. Here’s a video to start with, this one has lots of questions: