There are two types of threats to computer Security - major (criminal) and minor (nuisance).
Criminal threats
Methods include e-mails, picked up by a site visit or direct IP address attacks (attacks on your computer without any action on your part).
Nuisance Threats
What is a Virus?
It's a small computer program that a malicious person (criminal)
has written that will damage your computer and either make
it inoperative and/or cause it to send e-mails to others
to propagate itself. You can "catch" it like
a biological virus from e-mails, removable media (USB
drives, floppies) or web sites. It can also be
put on your computer by a direct IP attack although this is
uncommon - criminals usually use that approach to steal your
identity or personal information.
Free scanners are available from:
The most popular browser is Internet Explorer - that is one reason it is the most prone to the risk of attack. The other reason is that it alone allows operation of Active-X controls. These are downloadable programs that will run on your computer. Useful if they are invited - really bad if not. A much safer browser is Firefox although you need to keep Internet Explorer available for the odd occasion when you DO need to run an Active-X control (such as to run some of the scans in the previous section). More on the subject here.
Note that any free anti-virus program is not as effective or comprehensive as one you pay for - no surprises here. But free programs are often good enough - especially for home users.
If your computer is infected and the virus prevents you from going to an Anti-Virus web site (like any of the above), you'll have to modify a Windows file. Details here.
More comments on program speed (or lack of it) here.
A firewall is software or hardware that prevents your computer from receiving or sending (to an outside person) anything that you have not requested. These criminal programs are often spyware intended to steal your identity but other types are possible. Some software is one-way only - that is, only manages incoming requests such as occur via hackers scanning the internet for vulnerable computers (direct IP attack). The illustration on the right applies to these one-way firewalls.
Two way firewalls also block outgoing requests not obviously related to incoming requests as might occur with a program planted on your computer via a Trojan. This is a program that comes in to your computer looking benign but which conceals a program that sends data back to its originator.
The best Firewall by a large margin is a hardware
firewall. These are very simple devices that go between
your modem and computer and handle internet traffic.
If the traffic is valid, it will relay it to your computer.
Most routers come with a firewall so add a router to
your system even if you don't have a network! Unfortunately
this does not apply to dial-up users.
More
on routers below.
Another solution is to use a Security package such as that offered by Eset. This adds a firewall to their Anti-Virus package. Similar packages are available from McAfee and other Anti-Virus vendors. If you have Vista, you can activate the built-in Firewall for outgoing traffic but it's not recommended because it's too complicated. [I would ask, if you have effective incoming control, why is outgoing protection needed?] There are also stand-alone Firewall vendors such as Zone-Alarm - any would be better than none.
Definition of Spyware
Spyware is a malicious program that is installed unknowingly
into your computer with the capability of capturing
stored information and Internet usage and sends it
back to its (the spyware's) originator. Spyware has
been known to collect confidential information such
as credit card details. Spyware is at the root of
cyber-identity theft. Also, some spyware turns your
computer into a zombie owned by the hacker and they
make it send spam to people.
There are a two types of Spy Ware:

Cookies
These are harmless. They are placed on your computer by web sites
that you visit. Their intent is usually to allow a site to know when you re-visit
them. You may want this since they can remember your login information, shopping
preferences etc. On the other hand, you may not want someone knowing that you
visited certain sites. You can stop all cookies by adjusting your browser.
For example in Internet Explorer, go to Tools>Internet Options>Privacy and
adjust the settings. Controlling Cookies on Firefox is much easier (more).
Tracking Spy-Ware
The most common is the type that is often included with programs that
you have willingly installed. The installation program for the software not
only installs the program you want, but also installs additional tracking
software without your knowledge.
Some is relatively benign and simply wants to target their advertising better. But another more malicious type installs a program that monitors key strokes (e.g. bank account passwords) and sends them “home”. This spyware is a type of virus and most current virus programs will stop these.
Stop Spyware
If you would like to get yet more information on Spyware detectors, the Spyware Warrior has a large amount of data and conducts regular tests.
Is the process of "phishing" for people who are trusting enough to give their personal banking passwords etc to an unknown person on the Internet. Of course they think they do know the company asking for info but that's the scam.
The way it works, a spoofed website is typically made to look like a well known, branded site (like ebay.com or bmo.com) with a slightly different or confusing URL. The attacker then tries to trick people into going to the spoofed site by sending out fake email messages or posting links in public places - hoping that some percentage of users won't notice the incorrect URL and give away important information. The URL displayed on the link is different from the one you end up at.

The only sure defence is to know that banks and financial institutions don't do this sort of thing. So ignore it - delete the e-mail. If you are really concerned, phone the bank you believe has sent the message and ask them!
Other ways that are suggested, such as using the latest version of Firefox (3.0) or Internet Explorer (8) are not good enough. And refusing to do banking or Financial transactions on the Internet does not solve the problem - you can still get an e-mail from "your bank" asking for (e.g.) your Account number and ATM PIN number. The ONLY answer is to know that Financial institutions never send you an email asking for confidential info - if you get an email that appears to break this rule - delete it.
Many Anti-Virus/Anti-Spam programs will treat these emails as a virus and delete them but some get through.
Since Phishing is a form of an Internet Hoax, if you have not done so already, see our discussion of Hoaxes.
Ad Ware
Adware programs display advertising content on your computer without
your consent or direct knowledge. Often times this in the form of popup
windows that just drive you crazy. Pure Adware is not a risk and just
an annoyance. But sometimes it also includes spyware. In either case,
it uses up bandwidth and memory and can slow your computer to a
crawl.
In general, there are two kinds of Ad Ware:
If you run any spyware detector, you will generally catch these as well. Be sure to also download and use Microsoft's Defender program.
The most common way that the worst AdWare is delivered is using the ActiveX controls in Internet Explorer. A good preventative measure is to disable ActiveX in Internet Explorer (details here) or to use Firefox which does not use it. More.