What are some things to know when going on your first international trip? [closed]

You asked for a more general approach, so:

Rule Number One: Inform yourself about your destination.

Inform yourself about the people and their customs(!) and the respective laws(!!). This cannot be stressed enough because there are still people out there who believe that they can behave like in their home country and that the home law still applies. This attitude can kill you or give a very long prison sentence in countries like Singapore or Saudi-Arabia.
No, "I did not know that!" does not work. It is also not recommended to puff up oneself and believe that problems are going away if you complain loud enough.

Important is at any case the location of embassies (if you lose your passport or need general help from your home country) and how ambulance, police and transportation is working in the destination country.

Rule Number Two: Get all documents.

Everyone knows that you need a passport, but there are often other documents needed, so I give a short list of the ones who are often forgotten.

• Visa: As everyone here knows in painful detail, people try to travel to countries where a visa is needed and already bought a flying ticket. Then they are horrified that they do not get a visa and their ticket is worthless. Don't do that, get first the visa, then the ticket.
• International Drivers Permit: You want to travel inside the country by car? While there are countries which allow you to drive cars with your home license for a limited amount of time, for most countries you need an IDP which allows you to drive cars. Don't forget Rule No. 1: Inform yourself about the traffic laws and the traffic situation.
• Vaccination certificate. Some countries only allow people to enter which have been vaccinated against specific diseases.
• Credit card/Debit card/Cash. While you don't need a credit card at all in e.g. Germany, holiday in the USA will be almost impossible without a credit card. Some third world countries do not accept credit cards at all (and if they accept it, watch out. One joker in a bank (!!) tried to booked the money two times). Sweden on the other hand is almost cashless. So inform yourself what money form is available.

Rule Number Three: Don't forget important things and arrange a channel of communication if things run bad.

Because you cannot get things once your plane lifted off, you must be sure that you have everything inside your luggage. I have a list of things which I tick off when I travel. Please also look that you don't put forbidden things in your hand luggage which will be confiscated at the airport. I also have a list of phone numbers/emails of different people if something goes awry and I need help or inform others what happened (Or if something happens to me, police/ambulance can contact my contact persons). Don't use a single person because it is a single point of failure: The person can get sick, have an accident, whatever.

Have a nice holiday.

The UK and Ireland are both in the Common Travel Area, which is an "open borders" area agreed to by the UK and Ireland. As a result, it is not required for you to bring your passport, but just photo ID. However, note that some air carriers (eg. RyanAir according to that article) may require you to bring a passport anyway. Bring yours, and keep it with you at all times.

If you have an ATM card, you should be able to withdraw Euros in Ireland from your UK bank account. Notify your bank first that you are travelling, to make sure they don't block your account for possible fraud (seems unlikely between UK-Ireland, but you never know what might trigger a fraud alert). If you have a credit card, it should work with no special action required.

Many great answers already here. Some more points on “arrange a channel of communication”:

• If you want to take your mobile phone with you, you should consider the following: Find out if your contract supports roaming (use in other countries) at all, and what it costs. Incoming calls cost, incoming SMS cost, calls being redirected to the mailbox may not cost or may cost twice (once for redirecting to the other country and once for redirecting back), you may want to disable it. There may be substantial additional costs for the usage of data. Find out if your holiday location offers free wifi, and at what speed. Some may say “free wifi” but data rate is so low you cannot skype/whatsapp call sensibly. I never tried it but it is also common practice to get a local prepaid card at your destination country. Some phones support multiple SIM cards which makes this easier. For US/European travellers: Cell phone radio frequencies differ in US and Europe, so some phone handsets may not work at all when travelling between them. In Europe and in general cell phones have SIM cards, in the US not all. In cell phones without SIM cards obviously will not be able to use a local SIM card. Inform yourself before you travel.
• Find out how to call your home country. In all Europe, this is usually double zero, international code, full phone number without first zero. There are differences in other countries (I know of USA, Chile, Italy).

As British/EU citizens travelling to Ireland, you shouldn't have too many difficulties - no visas needed, they speak English, and your phones and bank cards will almost certainly work in Ireland just like at home, though you will need to 'convert' your phone numbers to international codes (ie. 01234 567890 will become 0044 1234 567890).

Do a bit of research before you go. Assuming you are travelling by air, find out how you will get to and from the airport in the UK; and the same in Ireland - Dublin airport has various bus lines and of course taxis ready to take you into the city centre. The airport also has ATMs, so you can grab some Euros to pay for the bus or taxi. Find out the address of the place you are staying and find out how to get there. A taxi will take you straight there, but a bus from the airport might drop you a long way from your accommodation.

Try to travel light. You don't need to take your entire wardrobe and the entire contents of the bathroom; and don't pack away anything you might need during the journey (passports, tickets, money, phones, medication, etc).

Airports are restrictive on what you can take through security and onto the plane, so find out what those rules are. No one likes having their stuff confiscated by security.