Becka,
Not to worry, I'm sure the group here will be able to help get your travel arrangements sorted.
To begin with and especially as this is your first trip there (or so I'm assuming), I'd highly recommend packing along a copy of either the Paris or Pocket Paris Guidebooks, as there's a LOT of information there which will help your sightseeing to go more smoothly. I was back in Paris in June, and referred often to the Pocket Paris book (even though I'm quite familiar with Paris). For example, some of the Museums are closed one day a week, so it's important to know which day that is.
In terms of getting around, the Metro is by far the easiest and quickest method. If you're not familiar with using subways, some homework would be prudent (it's not really too difficult, and I'm sure you'll get used to it quickly). I usually buy a Carnet (10 tickets) which often covers my transportation for the majority of each trip.
I assume your flight will be arriving at Paris / CDG? One of the quickest ways to get to Paris from the airport is to use the RER "B". It is possible to buy tickets for that using Kiosks, however they only accept Euro coins or "Chip & PIN" credit cards, so you may have to wait in a queue at the ticket office. You may find it helpful to have a look at the excellent Paris By Train website.
For using the EuroStar to travel from Paris to London, you may find it helpful to have a look at the excellent Man In Seat 61 website. You'll be departing from Gare du Nord in Paris and arriving at London St. Pancras. Note that you MUST check in for that at least 30 minutes prior to departure or you won't be riding. I'd suggest leaving lots of time, as you'll have to go through airport-style security as well as clear U.K. Passport control in Paris. Buying your ticket well in advance will provide the cheapest prices, but note that tickets are often non-refundable and non-changeable once purchased, so choose carefully!
If you're planning to visit a lot of Museums, it would be a good idea to pick up a Paris Museum Pass as it will minimize your time waiting in queues. It will likely be VERY busy in June, so it's best to tour as efficiently as possible. Also, be sure to wear a Money Belt and be vigilant for pickpockets and scammers, as they WILL be plying their "trade".
Which part (Arrondissement) of Paris are you planning to stay in? All of us here have individual preferences, and I like the Rue Cler area in the 7th, which is close to the Eiffel Tower. Are you planning to stay in budget hotels or Hostels? What are you planning to see while there? Some additional information will help the group offer more specific travel advice. It will be easier to provide more specific advice on getting from the airport to the hotel once you've decided on which part of Paris you'll be staying in.
Good luck with your planning!