Just be direct. Give them your resignation letter and tell them you're resigning and that your last day is in two weeks or whatever. It's been a great experience and thank them for the chance to work there, but it's time for you to move on.
Do include details like whether you intend to give two weeks' notice if you're willing to stick around to train your replacement or whether you'll be leaving effective immediately. Don't go into why you hate your job, how you're so happy you're leaving, and how you hope they have a terrible fiscal year without you.
Just keep it short and sweet, this is your resignation and ___ will be your last day. Date it, sign it, and be done. If they want to know, they will ask and you can say something then, if you want.
Dear Recipient's Name, Please accept this letter as formal notice of my resignation from Company's Name, effective two weeks from today. My last working day will be Last Working Day, Date. I've appreciated the chance to work at Company's Name and grow professionally.
In addition, I have three unused vacation days and plan on using those on (list the dates). Thank you for everything you have done to help my career and make my time at (Company Name) such a pleasure. I truly wish you and the organization all the best in the future. Again, this is just a resignation letter example.
If it's a short vacation like 1 to 3 days, you should give notice 7 days in ahead of time. If it's a long vacation like 4 days to 2 weeks, you should give at least 3 weeks notice ahead of time. But those are a rule of thumb.
Yes. It's completely fine to give your notice after a vacation.