Here is a brief instruction on how to use an ATM:
When you find an ATM, first check if it accepts your card. Usually, the ATM shows which card it can accept (e.g. Visa, Plus, MasterCard, etc...) on the edge of the machine.
If the ATM accepts your card, insert your card and start the transaction. After the ATM recognizes your card, the screen switches to a transaction screen.
First choose a language you are most familiar with. Some ATMs display the language as a flag. In this case if you prefer English, choose the UK flag. Enter PIN if necessary.
Then it might be slightly dependent on each ATM, but you should likely choose withdraw. Then choose which account you withdraw from. It is likely savings account but it depends on your bank and your account.
Enter the amount you want to withdraw. Enter PIN if necessary. If you get asked about the conversion, choose "no" (or "without conversion") and make your bank/issuer convert it for you.
After that, the ATM will get you money. Pick up the money and your card, and it is done.
Also, pay attention to people around you while you are using the ATM. And also pay attention to the card slot in order to avoid skimming. And as @Hilmar said in the comment, you shall inform your bank and/or credit card issuer that you are going to use it abroad in case it is blocked by the issuer for a potential fraud.
As to the amount of money to carry, it depends on each country and city, and also your travel plan. I always use a credit card if possible, so in countries that have high credit card acceptance (Estonia, Poland, South Korea, etc...) I only carry one small bill (around US$20). In other cases, I usually carry about US$20 up to US$100 and put emergency money (about US$100 to US$300) in my room.