if I buy bitcoins, what will I need to know about the software involved?

You don't have to know anything really, if you don't want to.

and where should I keep my bitcoin wallet?

If you don't want to learn about the software or how to keep your wallet secure you should try to find the most reputable e-wallet and keep your money there. People will have different opinions on which one is the safest so have a look around, read forum threads, use something that is well established. MtGox is one option that is well established and is also the exchange with the highest volume.

I have a home computer and I have a Google account. Can the latter be used?

If you don't want to use an e-wallet you could download the official client from bitcoin.org and store your money in its wallet. Your money is then stored in a file on your computer. You could use your Google account to backup that file (your wallet). That would basically mean that the same money is stored in two places - on your own computer, and in your Google account.

What security issues are involved?

If you choose the option of downloading the client it means that anyone who gets ahold of your wallet file can spend your money. If you have uploaded the wallet to your Google account that simply means that there are two places to rob you. It would be enough for the thief to get it either from your home computer or from your Google account.

There is an option in the client to encrypt the wallet using a password. That way anyone who gets ahold of your wallet file can't use your money unless they also know your password. Things to keep in mind here is that if you have some malware on your computer it is possible that it could sniff that password as you type it and then the encryption won't help you. Also, if you forget your password your money is gone. There is no way to recover it.

If I'm travelling and far from home, how would I have access to my bitcoins?

Then the simplest way would be to use the e-wallet option.

It depends on how much security you want. If you only have a few bitcoins to get started you can get by with only medium security, for which simply installing the software or any eWallet will be fine. (Just be sure to tighten up security before you invest your entire life savings into Bitcoin). For absolute convenience you can't beat Instawallet.

When it's time to add more security, keep in mind you need to protect against both loss and theft, and that the former is much more likely. So err on the side of having more copies with more availability for your data.

1. The first step will be to locate the wallet.dat file on your computer and include it in a routine backup procedure. Once a week should be fine. If you change computers make sure to take it with you. If you're using an eWallet, store your password in several safe places.
2. The next step up is using the new wallet encryption feature. This makes theft harder but loss easier, so make sure the password is written down in a safe place. Note that this isn't airtight security, you're still vulnerable to keyloggers and other sophisticated infections.
3. The next step is to separate your everyday use wallet from a savings wallet. This can require a bit more skills to do properly - the basic idea is to keep the savings wallet in a secure machine (preferably Linux) and not let it get in contact with a vulnerable system. You'll only spend from this wallet occasionally so it's ok if accessing it as a bit of a hassle, depositing funds in is easy. Make sure to take precautions against loss.
4. In the future you will also be able to incorporate two-factor authentication to your wallets, which when done correctly can give very high security.

To access your bitcoins while traveling, you can use either a remote login software such as LogMeIn, or an eWallet (memorizing or taking with you your password). Even if you don't use an eWallet normally, you can transfer to one how many bitcoins you think you'll need.

You really don't have to be too computer savvy to own & trade in bitcoins. If you are a newbie, this explanation might help you figure out how to participate.

A "wallet" is where you store your bitcoins. You can have a wallet on your computer, or you can have a web-based wallet online. A great comparison is to think of email. You can use Outlook or Thunderbird where all the email is actually stored on your pc, or you can use gmail and have your email stored in the cloud online. The online wallets are called e-wallets. The little programs that run in your pc or smartphone are just called wallets (or bitcoin clients).

Online wallets are as easy to set up as, well, a gmail or yahoo mail account. In a few minutes you are all done. Your e-wallet "account" is created and ready for transactions.

If you choose to create a wallet on your pc, the setup process takes a bit longer. As of this writing, (april 2013) it takes about one minute to install the bitcoin client on your pc. But it takes about two days for the client to download this huge file called the blockchain. Your client won't show any deposits to your account until the blockchain is fully downloaded and "synchronized."

The blockchain is this huge record of EVERY bitcoin transaction that has taken place, ever! It grows and grows with each transaction. It is "synchronized" with every other bitcoin client (with some exceptions) A copy of it exists on every bitcoin client in the world. Why? because by publishing the transaction block to every bitcoin client, "they" (the enemies of bitcoin) can't just take out one computer or web address and kill bitcoin. "They'd" have to take out every computer that is running bitcoin.

This concept implies a big vulnerability not of wallets, but of e-wallets, the online wallets. E-wallet service providers are vulnerable to cyber attacks, etc. And if they decide to "temporarily suspend operations" or plain old go out of business, then you could lose some or all of your account balance.

Please note that another answer in this thread refers the user to get an e-wallet account with INSTAWALLET.COM. Well, as of this writing, Instawallet.com has ceased operation and is giving out "refunds" and they may or may not be complete refunds. (story: http://techcrunch.com/2013/04/03/bitcoin-instawallet/)

So there is risk to using online e-wallets. But not so with the regular wallets that are stored on your pc. They have a different kind of risk. Basically, the wallet in your pc is as vulnerable to loss as the cherished photos and other documents you keep on your pc. If your pc is stolen, or if the hard drive goes out, then you are up the creek... unless you have backed up your wallet. Like your photos, it's just data and it can easily be backed up.

So are you computer savvy enough to own and trade in bitcoins? I will continue to use the email metaphor from above. If you think you are computer literate enough to install an email client such as Outlook, Thunderbird, or Eudora on your pc, and if you do regular backups of your precious files, then you have what it takes to go with an original bitcoin client, such as Bitcoin-Qt. (Get it from bitcoin.org) Otherwise, if you prefer the ease of use of gmail, and if you are willing to accept the risks outlined above, then go with an online e-wallet. (one is blockchain.info)

Here is an excellent primer to Bitcoin... "What it is, How it's used, and Why you should care."

best wishes!

If you set up a mtgox account to buy some bitcoins, you can store them there for the time being. If you want to get setup with a wallet on your desktop, you can follow the instructions at https://en.bitcoin.it/wiki/Getting_started

It basically entails downloading the client, and running it on your computer. It will create a wallet for you, which stores your account(s), addresses, and bitcoins.

You can then tell mtgox to withdraw your bitcoins to your bitcoin address. This sends the bitcoins to your wallet on your computer.

As for travel, you can keep the bitcoins in an ewallet, mtgox, or even a mobile wallet on your cell phone.