I am having issues when it comes to how time passes in the book I'm writing. I usually find myself describing the day from start to finish, and that's just useless material since nothing relevant happens 24/7. But I can't find a way to skip one week, one month, or whatever without making it awkward. Any advice?
Time skips are used all the time. The key to doing it well is wrapping up the previous scene.
Your book (or a screenplay) is essentially a collection of scenes. Usually, early in a book the author establish a "rhythm" so the reader expects the scenes to be either in a continuous flow, or there is a typical timeskip of hours or days between the scenes. If one scene is immediately flows into the next one, there is no need to wrap it up. But the longer is the coming timeskip, the more thorough wrapping should be applied.
For example, two characters meet and talk to discuss some issues. Without a timeskip, you can leave them at midsentence, not resolving any of those issues and any questions that the reader might have on his or her mind. But if the meeting is over and timeskip is coming, you need to explicitly signal that, and either resolve the issues or mention that the issues are left unresolved.
Same goes for "cliffhangers", when the author deliberately leaves unresolved conflicts when closing a scene. First, you accentuate the cliffhanger, but then in the next chapter do something like switching the POV, and not even mention how much time has passed since the previous chapter end.
What exact words should you use to describe the timeskip is, imho, a secondary problem. If the rhythm of scenes is established, the author does not even have to mention the amount of time passed. It could be a day, or a week, or a month - a properly wrapped previous chapter, taken together with the opening events in the current chapter should give the reader an idea of how much time had passed. It could be two days or two weeks - is this really important to the story?
Skipping hours, days, months, even years, is standard in fiction. In fact, it is narrating non-stop through the tedious everyday that's non-standard.
How do you skip time then?
Think of every scene as a mini-story. It should have some sort of opening, some "meat", and then it gets wrapped up (as @Alexander says). Then the readers know it's time to jump to the next mini-story. There should be some arc connecting those mini-stories, some logical progression between them. Same way there is a logical progression between the paragraphs of an essay, while each paragraph is also its own mini-story.
As an example, let us look at some time skips in The Lord of the Rings. For simplicity's sake, I will focus on one chapter alone: book 1, chapter 3 - Three is Company.
The previous chapter was all about Frodo learning about the Ring, It was wrapped up with:
'Me, sir!' cried Sam, springing up like a dog invited for a walk. 'Me go and see Elves and all! Hooray!' he shouted, and then burst into tears.
Chapter 3 opens:
'You ought to go quietly, and you ought to go soon,' said Gandalf. Two or three weeks had passed, and still Frodo made no sign of getting ready to go.
There is a logical progression: from realising what Frodo has to do, to making no progress with doing it. There is also a mention of time, so the reader knows where he's standing. And the next scene is opened with the bit of conflict about Frodo's delay.
The scene is wrapped up with the issue of the delay being resolved - a decision has been reached. The next scene, again, by logical progression, opens with the consequence of that decision:
One summer's evening an astonishing piece of news reached the Ivy Bush and Green Dragon. Giants and other portents on the borders of the Shire were forgotten for more important matters: Mr. Frodo was selling Bag End, indeed he had already sold it - to the Sackville-Bagginses!
The scene of the hobbits' reaction to the news wrapped up, there is nothing more to tell for a while. The next scene starts:
Gandalf stayed in the Shire for over two months. Then one evening, at the end of June, soon after Frodo's plan had been finally arranged, he suddenly announced that he was going off again next morning. 'Only for a short while, I hope,' he said.
The focus of this scene is Gandalf's absence. Within that scene, time passes:
At first Frodo was a good deal disturbed, and wondered often what Gandalf could have heard; but his uneasiness wore off, and in the fine weather he forgot his troubles for a while. The Shire had seldom seen so fair a summer, or so rich an autumn: the trees were laden with apples, honey was dripping in the combs, and the corn was tall and full.
Autumn was well under way before Frodo began to worry about Gandalf again. September was passing and there was still no news of him.
With these examples before you, you can see how time can be skipped between scenes, or within a scene. Treat each scene as a mini-story: figure out what it's about, and tell that. Then progress to the next mini-story in a way that makes logical sense. "Logical sense" should be guided by narrative, by what is the story you're trying to tell. "What happened next" is secondary: it might be not interesting and skipped entirely.
If your issue is with the telling of the passing of time, then you could try to show it.
This is done by relating events or facts that the reader know would take a certain amount of time to happen.
I give you some examples:
One season, or one year:
The trees were already pushing their flowers out of the buds when MC arrived at Famous Village.
A few years:
The last remedy to lice was to shave her head. She cried and MC could do nothing but to stare at her bald head from the window. "Hello" she said one day. She had grown her hair to the shoulder, and wore it in tight locks.
A few decades:
Eclipses are rare. It was the second they were looking at, and mom's hair had turned white in the meantime.
The sow had made three litters. And from these, one piglet had grown into a fat and prolific sow too. MC was struggling to keep her last newborns at bay.
Couple of days/weeks:
The coach returned to London ten times before it brought news of MC's uncle sickness.
The door slammed. The feet rushed down the stairs. There she was again, opening that damned door.
Readers are used to reestablishing the time, place, and perspective when a new chapter starts. If your writing has chapters, and usually follows the characters moment to moment, a chapter break is a great opportunity to kick time forward. If you don't have chapters just a *** breaking the text can let the reader know that the camera is moving to somewhere new.
Once you start a new chapter treat it the same was as when you started your book. Kick off with something interesting and then in a few lines give some hints to reestablish time and location.
"I still can't believe that shootout was only two days ago, it feels like it was in another lifetime."
"So this is Paris? OK I know this is just an airport, but I expected more."
If you are finding that you need time-skips too often you may want to make other adjustments. Maybe jump forward in time to another plateau and handle the conveying the missed information through dialog.