Are there free tools (preferably online) that will tell me what other people are paying for certain keywords? I am thinking of doing some advertising, and I'd like to know what price would make sure that my ads are visible, etc.

nope, no tools available. Every person will have different quality scores so it's impossible to say how much they pay. You just need to try it and see how well your terms perform. you used to be able to on Yahoo until they launched their new system, but this is no longer available.
Set yourself achievable goals. Do not rush in bidding $25 a click when you only make $2 profit per sale. Use common sense to see how you get on. Take is easy at the start and if your successful, turn up the advertising spend.

Briggidere is right. It's hard to know an exact amount. If you have a keyword-targeted Adwords campaign, at least it will tell you if your keywords are triggering your ad to be displayed. It also tells you what the minimum bid is for each of your keywords. However, even if your ad is not displayed on search result pages, it could very likely be displayed on the "content network". For example, I usually only bid 5-10 cents per click and I've discovered that I have more success on the "content network" than on the search result pages. Unfortunately, with the content network, there is no way to know which individual keywords are working better than others. Sometimes it's just a guessing game, but don't give up. Keep trying new things until you find a formula that works for your particular campaign.