I have a Linksys wireless router. How do I encript my network?

I seriously think a good place for you to start would be google
There are many things to consider and many ways to go about this that have been discussed in many places.

Whatever you do, don't use WEP.

Indeed. Try WPA2 if you can. If any devices encounter issues with WPA2, use WPA.

In a home network WPA is USUALLY more than sufficient.
In a corporate of office environment, then the overhead associated with WPA2 may be necessary in order to protect long term assets.
The issue with WEP is that there are several utilities widely available that will permit a quick "crack" of the WEP key thus allowing a malicious user to actually see all of your information, infect your systems, or hijack the same. WPA requires much higher levels of cracking technology, and in a home or small business, most likely never be brought to bear.

If you work from home, and have a great deal of proprietory information on your home systems that could be used against you or your company, then you may need to escallate to the WPA2 standard.

The main reason I would try to use WPA2 first is because it has the Advanced Encryption System (AES) which is far more secure than TKIP. TKIP is basically an enhanced WEP protection where AES is all new for WPA2. For home networks, use WPA-PSK or WPA2-PSK (Pre-Shared Key, also known as "Personal").

The only issue I was trying to point out is that there is a processing overhead differential of about 30% between WPA and WPA2. In long term, or high risk connections I think that the overhead is worthwhile, but for the average home user, WPA is much more secure than WEP with a minimal (mayhap 10%) overhead increase, and the time it would be required for someone to sit in front of your house in order to crack WPA would require a major output in computer resources that for most home owners, and to a certain degree SMBs need to be worried about.
Having said that, I do recommend that VPNs use at least AES-256.

I can't say I've ever noticed a difference in throughput between them. Certainly not to an extent that warants giving up the extra security. I can't use WPA2 here because my router hiccups with it (I think the model was pre-2006). Newer networks work great with WPA2.

Ford,
I didn't specificly state a "throughput" issue, but a processing overhead issue. The impact on throughput is minimal as it only adds a few bytes to the header (unless of course you are in a situation of very high packet fragmentation, in which case the throughput could be majorly impacted), it is the actual encryption and decryption of the packets in the wireless router and on the host that increases the overhead. This may have been what was causing the problems on your older router. Even if it supported the standard, the load was too high for the processor/memory to handle and you would overrun your buffers, thus causing hiccups.

Naw, it is consistently bad. It doesn't work most of the time regardless of how much activity is going on in the network. It just isn't fully Wi-Fi Certified is what I think.