I haven't used e-mail encryption for a while, I am not sure how exactly to set it up, but once it is installed, it's very easy to use. Here is what I know, though you will need more details; perhaps someone here can add them.

First, you need a mail client that supports encryption. I use Mozilla Thunderbird as an e-mail client, and there are some plugins that support encryption. I don't have recent experience with them, so I don't know which one to recommend. (After short googling, Enigmail seems to be a popular choice.)

Second, to send encrypted e-mails or digitally signed e-mails, you need a public/private key pair. There are some softwares that will generate such pair for you, and you will add them to your mail client. Additional layer of security is if you have a certificate confirming that this is your public key. (Such certificate protects you against a kind of attack where I would send your friends an e-mail pretending to be written by you, including my public key pretending that it is your public key -- or I could do the same thing by hacking your webpage, if your public key is published there.) Last time I tried this, there were some certificate companies that would give you a free certificate, but only for non-commercial use and with validity of one year. Another use of certificate authority is that if someone steals your private key, you can publish an information that people should not use the corresponding public key anymore.

Please note that encryption and digital signature are two sides of the same coin. Simply said, encryption (based on public/private keys) is "everyone can write, but only one can read", and digital signature is "everyone can read, but only one can write". Actually, there is no difference between private and public key -- they are just two numbers that together have some mathematical property, and their role in this property is symmetrical: if you encrypt something with public key, you can decrypt it with private key (this is called encryption), and if you encrypt something with your private key, you can descrypt it with public key (this is called digital signature verification).

This is the difficult part, but once it is done, using the system is the easy part.

If you receive a digitally signed message, it will have an icon (colored pen). By clicking on the icon you can add the person's public key to your database. (You should be pretty sure that the mail was really sent by that person, not someone pretending to be them.) If you have someone's public key in a database, when you write them an e-mail, you can select to send it encrypted. You can also select to digitally sign your e-mails (which will allow other people to send you encrypted messages). If you receive an encrypted message, it will be automatically decrypter for you.

It really is as simple as checking "sign this message" and "encrypt this message" when sending mail, and clicking "import this signature to my contact list" when receiving a signed mail. Otherwise it is like normal e-mail use.

GPG seems to be gaining mindshare. It is an open-source set of libraries and command line tools that inherits a lot of the interface from PGP (which is proprietary).

I have used the Cryptophane interface on windows and it makes it pretty easy to generate keys and manage them in your local keystore as well as to sign, encrpyt and decrypt arbitrary text. This would get tedious if you did a lot of email though but based on what you described I think it would work well for you.

Here is a link to other front-end tools for GPG: http://www.gnupg.org/related_software/frontends.html

I'd also recommend GPG, especially if you use (or could switch to) an email client with a decent plugin for it.

One note: you still need to securely establish common keys beforehand; public key encryption just makes "securely" easier. To attack a symmetric key encrypted communication, you just need to be able to eavesdrop on the key and the encrypted content. To attack a public key encrypted communication, you need to be able to eavesdrop on both public keys, block the true public key messages from reaching their recipients, inject false messages with your own public keys, and then eavesdrop on the encrypted content. None of the industrial-scale solutions for preventing this (certificates, web-of-trust, etc.) are very satisfying to me, but "call your buddy on the phone and spend 20 seconds reading key hashes out loud" is fine for personal security.

There aren't any existing websites I know of that do this. I've played around with a GPG plugin for Thunderbird, but I never used it enough to make it worth keeping. It was pretty straightforward to use, so I'd give it a shot.

Enigmail

Thunderbird

For email, the main problem is the automating the public key management. There is some hope here in the deployment of secure DNS (DNSSEC), which has the potential to automate the process so that everyone, by default, has a public key without taking any special action.

However progress is extremely slow and the incentives weak, so I would be surprised to see significant progress any time soon for email.

If you use Skype (and probably other proprietary systems, even your mobile phone) encryption will probably come as standard. There may however be back-doors, possibly allowing the provider, governments and law enforcement access. But it's better than nothing. The architecture of Skype, where the traffic passes through completely untrusted super-nodes (for example my computer!) pretty much demands the use of encryption.

Nothing to add at the moment that others haven't already. But I went through the same process myself (with GPG), and I have an interest in how to convey information like this, so please do not hesistate to say if any of the answers given are incomplete and I will try to fill in the gaps.