Ok. You are going to want to travel by train once you get there if you are planning on visiting more than a few cities, which I assume you are if you are going for a month. You get a Euro Rail pass, these are passes that will allow you unlimited rail access for 3 weeks or a month or so. Google it. They are about $300-$400 if I remember correctly, and do NOT exempt you from certain booking fees, so you do sometimes have to pay a $10-$15 booking fee. This pass will NOT work in England, Scotland, Northern Ireland, or Wales
You may want to fly in to Ireland, take the ferry across to Wales, then take the Euro Star from London to Paris or Brussels. your rail pass will not cover that train ride and it is quite expensive, but when I went I found that to be the cheapest way. Plus you get to see Ireland which is amazing, and the ferry is like a giant floating casino, its pretty cool.
Do not allow anyone you meet in a train station upon arriving in a town suggest/take you to a hotel. Do not allow taxi's to suggest a hotel either. Often they will make a commission which will be added to your bill, and the place will be shitty. I got lucky doing that in Rome but very unlucky doing it in Amsterdam.
Hostels are much cheaper than hotels, book ahead. For some reason many guide books do not include area codes with the telephone numbers, if you find a number doesn't work, look up the area code for the region in the back of the book or online. Occasionally you can get lucky and book many people into a hotel room for one, but don't bank on it, especially in Italy.
If you take shrooms in Amsterdam DO NOT take the whole dish. They will probably tell you it is a single dose, and it only looks so much because they are fresh (not dried), and you need to eat all of it to trip. I don't know what the fuck they are on but it is wayyyyyyy more shrooms than one person needs. I have confirmed this with a couple other people I know who had similar experiences.
If you are on a tight budget you may not want to go to England, especially London, as it is much more expensive than anywhere else in Europe and the exchange rate will kill you.
European officials are slightly more open to bribery than American ones and you may be able to buy your way on to a train for some extra cash. In some desperate situations that has saved me.
If you are feeling lost and want to have a friendly conversation in English with someone, find an Irish pub. Irish pubs in Europe generally have Irish people behind the bar and it can be a lifesaver if you are in Italy or somewhere with horrendous accents and just can't stand to not have a civilized conversation for another moment haha.
Have fun and be careful. (Western) Europe is generally pretty safe and as long as you keep an eye on your wallet and be smart about it you will have a great time.