Quoting Nng
However, just one problem. How much would all those activities cost? I'm guessing there isnt any fee to pay to enjoy a day hiking through the forests and things like that right?
Some activities are free. Some activities cost a little. Some activities are more expensive. You're right that a day hiking in the forests is essentially free. However, you may need to pay an entrance fee for the provincial/national park. Such is the case for Banff, for example. Last I went it was about $20 for a weekend. It isn't steep, but you should factor that in. Of course, if you decide to make a weekend of it, you will need to pay for your camping spot (by the spot, instead of the car, person, or tent, plus extra if electricity is required, usually; wild camping isn't permitted in the parks.) Firewood is sold for extra as well, so if you can bring your own, by all means use it. Open fires are not allowed. You must use a firepit. But they are premitted as long as a fireban isn't in place, so there is no need to go out and buy a camping stove or anything like that- maybe a few metal skewers for hot dogs/marshmellows, although plain old sticks work just as well. Definately rent a car for a trip like that. It is way too difficult to attempt that kind of trip by bus, and forget about by train. The train is very limited in Canada. So the cost of a car rental/hire must be factored in, as well. Plan for about $85 per day for a rental car, maybe less if you're lucky. You can also rent an RV, but I have never attempted that, so I don't know how much it would cost. There are RV rental places in Calgary, so when you get here, you can call them up and check (it is late in the evening here). An alternative is to buy someone's old beater through the Bargain Finder (found for pocket change at any 7 eleven convenience store), Craigslist, or Kijiji. Drive it around for a month and then sell it on the aforementioned places. You may even make a profit, but don't count on it. So that covers hiking and camping.
One thing that I recommend is the book, Don't go Hiking in the Canadian Rockies Without This, if you're into hiking. You can pick it up at any Chapters or Coles book stores in Calgary. It is an excellent guide that I have used over and over and over, and you will not be disappointed if you pick it up.
To go fishing, you need to buy a fishing license. It's been a while since I've gone fishing, but it isn't expensive, just around $15-30, I think. You can buy one for various lengths of time and you go to any registry office, or, more easily, any Canadian Tire store to purchase one. Then you just need a pole and some bait, all of which can be bought at Canadian Tire with the help of one of their salespeople to pick up the best bait for the river or lake you will be fishing in. Personally, I know fly fishing works best for the Bow.
Skiing/snowboarding is much more expensive. You will need to pay for entrance to the park, then equipment rentals, then lift passes, then accomodation if you don't want to be driving late at night/early in the morning, then a rental car. It'll be costly. If you go, go to Sunshine or the Kicking Horse. The best snow around. Some ski resorts have buses that charter people from the nearest city/town up to the mountain, Panorama being one I can recall, so you may be able to forego the rental car, and greyhound it in. Alternatively, look into cross country skiing. The Banff Nordic Centre is a nice place to go to, though they do have man-made snow, so traction is slightly different. It's not nearly as expensive (around $15 per person for rentals, and skiing is free, if I recall correctly), and you can easily go in in the morning, spend the day there, and drive home in the evening. You will definately be exhausted by the time you are done! Snowshoeing would be another inexpensive option, though I have never looked into it specifically.
Canoeing/kayaking is another inexpensive activity. Many of the motels along the lakes in the Okanogan let you use their paddleboats and canoes for free as long as you are staying there. Otherwise it would a nominal fee, a few dollars for fifteen minutes to half an hour, something like that. Kayaking is really easy and can be done on a lake without needing hardly a lesson. It's about $15/hour. Lots of fun.
Other lake activites aren't very expensive, either. You can rent jet skis, motorboats, waterskis, and so on. Or you can just go swimming (free) and sunbathing (free). Or get involved in a pick-up game of beach volley-ball (free)!
As far as mountaineering is concerned, or ice climbing, I have no idea of the costs of these activities as I have never done them. I have hiked extensively in the Canadian Rockies, but I have never climbed to the peak of a mountain, and it is recommended that you do not attempt this without a guide. My guess would be that this isn't cheap.
Horsebackriding. This can be really cheap, or moderately expensive. It really depends on who you go with. My horsebackriding experience, unfortunately, amounts to trail riding at summer camp. So I'm not exactly fit to quantify this one. One outfitter that seems reputable, as they have been around as long as I have, is Holiday on Horesback. I have heard several positive reviews of this company, and, like I said, they're practiaclly an institution, they've been around that long. Holiday on Horseback is basically a weekend-long trip on Horseback through the Rocky Mountains. You'll find brochures for it everywhere when you come here.
Skating. If it's cold, this will still be possible. It's free in Calgary at the Olympic Oval for an unperishable food item donated to the local food bank (I believe) or you can go to one of the many outdoor rinks (not guaranteed in the spring). My recommendations would be Olympic Plaza downtown (at night amongst the city lights) or Bowness Park, where there are firepits on the ice for skaters to warm up their hands and feet. Hot chocolate is sold at a little cafe lakeside. Both outdoor places are free. There also is an outdoor rink in Banff with mountains in the background, if you happen to be there and feel like skating, and its free.
Whitewater rafting. Companies abound. It can be pretty expensive. There is one that goes down the Fraser River that is really wild (includes waterfalls and everything) and includes a steak dinner at the end of the day. Though I haven't gone on this one particularly, I have family that has and they came back praising it, so it is safe for me to recommend them. Google whitewater rafting on the Fraser River to find them. Personally, I have gone whitewater rafting (with a different company), and I thoroughly enjoyed it, so if you get the chance, jump at it. It's worth it. You won't forget it! 
Have I listed them all? Well, I'm exhausted, so I think I'll leave it at that for today
If you have any more questions about things to do and cost, do ask.
Quoting Nng
How far are those places form one another?
Yeah, Canada is pretty spread out and is much bigger than Singapore! In fact, I guarantee that for the first couple weeks you'll feel like a bug here. Whenever I come back from an overseas trip to Canada, I am overwelmed by how big everything is here. We Canadians think of distance in terms of time, for instance. So it is a three hour drive from Calgary to Edmonton, for example. That's a little over 300 km. It's really about 350, but the speed limit is 110 on the highway, meaning you drive about a km every minute, or a little less. You'll find that almost everyone speeds on the highways, and that sometimes it is even safer to speed than to drive slower, because if you drive slower than everyone you end up becoming a bit of an obstacle. Besides that, you rarely get caught for speeding on the highways (not the case in the cities, however; watch out for radar traps!). Banff is about an hour's drive from Calgary (I speed, though, so maybe an hour and a half), so about 100-150 km. The ski resorts are a little further than that, but some are way into BC, so it could mean a day of driving before you'll get there, like Silver Star, for example. Forget trying to get to Whistler/Blackcomb from Calgary; that's two days of driving! Does that give you some perspective?
Quoting Nng
Would there be any age restrictions, certificate requirements and stuff like that to get up the rockies?
Age restrictions? Not to get into any attractions or national parks! The legal age of majority in the province of Alberta is 18. That means that you must be 18 in order to buy or drink alcohol, buy cigarettes, get into bars and clubs or casinos, or gamble. Some car rental companies will not allow a person under the age of 25 to rent a car. To get a driver's license, or to use your license from home, you must be 16. For a fishing license, you basically need the dexterity to hold a pole! I think the first time I went fishing, I was eight or something.
Other than a fee to get in, you don't need any "certificate requirements" in order to get into the parks. It may be beneficial, if you will be going to a particular park a lot, to buy a parks season pass. It'll be valid for the entirity of the spring and summer season. I buy one every year for Banff National Park because I go there a lot. They give you a thing that you just have hanging on your mirror and you get to skip the line (though it usually isn't very long) on the way in/out.
Well, if you have any more questions, let me know! 
Steph
edit: deleted some unnecessary text about a rooftop carrier!
[ Edit: Edited on 11-Nov-2009, at 00:19 by bluewaav ]