There are some things that are a pretty necessary part of your kit (the first 3), some others that will come in handy, and a few that will make you that extra step more prepared. It can be quite intimidating for most freshers on their inaugural dig. Hopefully this list of things to take with you will help a little.
1. A trowel
It's really important that you have your own, because you will have to go and dig on your own at some point, and no one wants to be the annoying person who keeps borrowing (and losing) other people's trowels...sorry! Some people scratch/burn their initials onto the handles as well, but they're more hardcore than I am. I should point out that this is not an ordinary garden trowel, and you should make sure it's a proper archaeological one. It'll have a flat blade, pointy at the end and on either side. Later on you may start using something called a leaf trowel, which is smaller and used for delicate work, but you certainly don't need to buy one.
2. Proper boots
3. Proper clothes
Shorts are good if it's quite hot, but if there's a lot of walking through thorny underbrush (which can happen often) they're very unpleasant. Lightweight quick-drying trousers, with many pockets, are what I prefer right now, usually combined attractively with an oversized grubby T-shirt. Shirts with pockets and long sleeves are also a good plan. Don't wear anything too nice, although I'd recommend taking one or two outfits that are nicer in case you go out in the evenings.
4. A tape measure
5. Hats and sunscreen
6. Laundry detergent/powder
In a little box or bottle. You will often end up washing a lot of your stuff in sinks and showers, so take a supply of laundry detergent. An extra sink plug often comes in handy for sinks that don't have them, but improvise with a thick sock if you don't have one. Yes, this works for a little while, but don't use a muddy one!
8. Chocolate and snacks
Wet wipes are a nice treat when you've got an inch of mud on you, but most archaeologists I know don't bother with washing their hands between digging and eating. You can be the exception. I'm warning you though, you can develop a cast-iron digestive system after a lifetime of being dirty. Personally, I only use them on my face.
Or mini pruning shears. Some plant roots go very deep, and you'll find them quite far down. They can be fairly thick and difficult to trowel around. Some form of gardening trimmer to chop through them quickly is great. You won't need these everywhere, but if you're going to be digging in an area of heavy vegetation they can save you a lot of time.
Remember, digs are really a 'work hard, play harder' situation. You form friendships that last for years, and the nights out with your trench mates (yes, we call them that) after a hard day's work are pretty amazing. Take a camera, and expect hundreds of photos and as many funny stories that you'll tell for ages after, reminiscing about 'that time so-and-so did [insert utterly bizarre and random activity] when we were in [insert exotic locale]'.
For tools and trowels, try
If you're looking for an excavation, there are plenty of field schools that will take freshers or untrained archaeologists and give you some training in exchange for the cheap/free labour. Try flipping through British Archaeology magazine, or surfing
Alternatively, google archaeological fieldschools. These aren't very common in India, but if you'd like to travel abroad and learn about being an archaeologist, they're ideal. They're based all over the place, so yes you can go to really exciting areas like Peru!