-Can I just buy something that connects to my cable modem?
Probably. Provided the cable modem has an ethernet output, not just USB.
-Do I need to replace the cable modem with a wireless modem?
Probably not.
-What pieces of equipment do I need, I hear of routers and hubs?
To connect more than one piece of equipment to most cable modems from most ISPs you will need a router which does NAT. These days routers come with several sockets, you'll only need an additional hub or switch if you want to connect more wires than that.
If you're going wireless you can get a router that contains the wireless gubbins, so no wires at all (apart from the one from the modem to the router) and no hubs or switches.
-Is a wireless connection as fast as my hard connection?
No.
-Are they reliable, or will I have to keep resetting it (saw a couple of threads about this)?
The internet is full of complaints about unreliable wireless connections. It is not full of complaints about unreliable wired connections. (Well, there is a little gotcha when making your own cables, but you only have to learn it once!)
-Are they easy to secure effectively?
It's supposed to be possible, if you want to get into that sort of thing, or hire a geek. I'm not sure I'd use "easy" as a description.
-If it's not secure does this provide a route into my home computer if someone is sitting outside or at worst can they only use it to get an internet connection?
It means they can walk all over all the computers and equipment in your home, unless you have taken further steps to protect them. All of which is possible, but you may not find it easy ... and if you get it wrong, you'll only find out when it's too late.
Basically your main protection from nasties from outside is the NAT function in the router. If you let a passer-by connect to your wireless network they've bypassed that and got you from the inside.
-Can you tell if someone is using it beside yourself?
Possibly. If you know what you're doing. And provided that they aren't trying very hard to hide themselves.
From the above you will probably be able to guess that I have wires all over my house, and the wireless function on my laptop switched off at the hardware level.