a) is there any need to pay if all you want to do is play the game you just ****ing bought?
If you've already the bought the game in a store all you need to do is register it on Steam, that's free. If it requires Steam to play the game will probably auto update to the latest patch before you can play, which can be a pain but there's nothing you can really do about it.
Steam is free to download and doesn't charge you a subscription, but you do have to buy a game if you want to play it. Once it's bought you can install it to any computer as many times as you want, but can only play it when logged into your account.
Also, a lot of games on Steam have demos, if you aren't sure if it will work, track down the demo and play that first, they're usually free.
b) how easy is it?
Pretty easy, when you buy a game Steam installs and updates it automatically. You just have to wait for it to be finished. Steam updates itself automatically as well, which is pretty handy.
Steam is a pretty stable system nowadays, it was kind of crash prone to begin with but it's mostly reliable now.
In use it's my favourite pc gaming portal. You get a server browser with internet, favourites, history, spectating and friends. Pretty much does what it says on the tin and pretty easy to use.
The friends/group system is easy to use, works like a cross between Xbox live and facebook, but geared towards getting you playing.
c) (and most relevantly) how safe have you all found it? is it easy to handle? is it a nuisance? (is that how you spell nuisance?) is there anything it helps to know before hand?
Never give out your password ever, I've never had my account broken into since 2004 when it opened, so it's pretty safe. Just again NEVER give out your password, even if it's to 'Valve' don't do it, if Valve want to do something with your account (this happening is exceptionally rare) they don't need your password, they have a masterkey so to speak.
Also never click on 'get game X free with steam' links on the web. If any freeplay sessions are coming up, they will be announced well in advance on Steam and automatically appear in your my games list when the event takes place, if that doesn't happen it's fake.
As long as you apply common sense it's a safe system to use.
My only serious problem with it is that you can't get refunds or sell games on. If you buy a game on it it's yours and that's an end of it. It's not a huge problem but it's something to be aware of before you commit to buying games, especially if you're not sure they'll work on your system.