“Sorry I’m late, guys, I overslept.”
“No worries. Let me bring you up to speed.”
You can say “I overslept” when you accidentally sleep later than you had intended to (for example, if you didn’t hear your alarm clock). There’s a different expression – sleep in – when you intentionally sleep later than usual (for example, on weekends or on holidays when you don’t need to go to work/school).
The expression “No worries” means “No problem,” or “It’s OK.”
To bring someone up to speed means to give that person updates, tell them the information that they are missing so that they can have a current understanding of the situation. Another way to say this is “Let me fill you in.”
“What are you up to next week?”
“We might go to the beach… but our plans aren’t set in stone.”
“What are you up to?” is an informal way to say “What are you doing?” This can be used to ask about what someone is currently doing in the present, or what they will be doing in the future (as in this example). You can also say “What have you been up to lately?” to ask about what the person has been doing in the recent past.
If something is not set in stone, it means it is not confirmed/final, and could be open to change.
“I didn’t read the book, I just skimmed it.”
“OK, but you got the gist, right?”
To skim a book or article means to look over it quickly. When you skim, you don’t read every word carefully, you just try to get an overall idea.
To get the gist of something means to understand the central/essential idea, even if you don’t know all the details.
“That presentation was way over my head.”
“Yeah, I found it kind of hard to follow.”
If something is over your head, it means it was too difficult for you to understand. The word way can be used informally to mean “very” or “much” – if something is “way too expensive” it means it is MUCH too expensive, not just a little bit too expensive.
The expression I found it in this context means “I thought it was” or “My opinion is that it was.” Hard to follow means it was difficult to accompany the flow of ideas; the person is implying that the presentation was rather disorganized and unclear.
“The third time he screwed up, I almost lost it.”
“You’ve gotta cut him some slack; he’s still new.”
The phrasal verb screw up means to make a mistake or do something incorrectly, resulting in problems or negative consequences. Another way to say this is mess up.
The expression I almost lost it means “I almost lost my temper (=got very obviously angry).”
The other person in the conversation says “You’ve gotta cut him some slack” – this means “You need to give him some extra freedom/patience, or treat him less severely than normal.”