English clauses can be analysed as having two separate orthogonal properties — there's tense, which is just past, present, or the structure English uses for future tense; and there's aspect, which includes perfect and continuous, in any combination or neither of them.
The tense refers to the time period in which the sentence is "set". When telling a story you'll usually use a bunch of sentences in the past tense, because the story happened in the past. Meanwhile when talking about things that are relevant now, you'll be using the present tense.
However, what if you're talking about something that's relevant now, but only because of something that has previously happened? This is the case where you would apply the perfect aspect to the present tense. The classic example is comparing the simple past "I ate", which might be part of a story but doesn't have any particular bearing on the present; with the present perfect (ie present tense, perfect aspect) "I have eaten", which is more likely to have the meaning of "right now, I don't need to eat (because I finished eating in the recent past and remain full)". The perfect aspect refers to something that has been completed, but the emphasis is on the relevance of the fact that that thing has been completed, not necessarily on the action itself.
These concepts can be extended to other tenses. For example, if you are telling a story in the past, you might say "I walked to the railway station. I had eaten that morning, so I didn't need to buy anything from the shop." The "story" is still all in the same past tense, but you refer to a previous action that has completed and that completion holds some relevance at that point in the narrative, so in that second sentence we use the past perfect (sometimes traditionally called "pluperfect").
Similarly you can have future perfect: "I will have had that meeting by then, so I'll know which colour wallpaper to buy".
The continuous aspect is another thing entirely and I think harder to explain, but it emphasises that an action is in progress at that time period. This is why it is mostly used where many other languages would use the simple present — for actions that are going on now, as opposed to habitual actions which English reserves the simple present for. So present continuous "I am eating". It can even be mixed with the perfect aspect, for instance if a task is done or perhaps interrupted but it's not the completion but the fact that the task had previously been in progress that you want to emphasise: "I had been painting earlier that day, so I was still wearing an apron when the doorbell rang".
Of course these are some very distinct examples, but native English speakers blur the lines between simple past and present perfect all the time, especially in some dialects and especially in colloquial speech. You will, in practice, find people especially from parts of the US saying things like "I ate already". But it's something a lot of native speakers really do use all the time without thinking about it or even consciously understanding it (I find most native speakers can't articulate what the actual difference is between simple past and present perfect, even if they can use them in sentences perfectly), so it's definitely worth learning.