One easy way to build an online store simply uses Paypal or Google Checkout, and a table you create yourself with all of your merchandise.
This method, of course, is not much fun. It’s labor intensive, and you do have to be well versed in HTML to make it happen (or else cozy with your editor). It’s also not very search engine friendly.
The good news is that there are easier ways that won’t break the bank.
Questions to Answer First?
Before we get to how, we have to tackle a number of other questions. Presumably, your museum already has an actual shop at the museum, which can help you get started.
What do you sell at your actual store? Books? Shirts with your logos? Rocks? Old fashioned toys?
Which items are your best-selling?
What will you do about shipping? (Shipping gets expensive, very quickly. Have you ever tried to mail something you paid 50 cents for? Unless it fits in a regular envelope, you’ll likely pay more to ship it than you did for the purchase.) (Note that some shopping carts will figure shipping automatically for you, or you can set your own rates based on whatever you want — with this method, you undoubtedly vacillate between coming out ahead or behind on any given order. If you’ve picked an appropriate rate, you should come out about even over the course of the year.)
Who is going to process orders?
This part gets tricky
If your best selling item in the store costs less than $10, or is available for less money on Amazon, you may need to rethink the online store. No one wants to pay $6 in shipping for something they paid $2 for, and if your primary stock consists of books that are readily available elsewhere, don’t count on many sales.
If, however, you have something unique (books printed by your museum/society, or locally handmade Indian jewelry, perhaps), it might be worth the time and effort to create an online store.
Requirements
To begin with, there are some musts for your store website, regardless of how you accomplish them:
- Restricted information must be passed through a secure, encrypted server (ssl — through the https: prefix, you’ll see the lock in your browser if this is the case)
- No login specific to your site should be required (login to the payment processor, if common (i.e., Google Checkout or Paypal in the U.S.), is okay)
- Don’t require information you don’t need (studies have shown that this will decrease your conversion rate)
- Buyers should be able to complete the sale in a minimum number of clicks (make “buy now” types of of buttons easy to find)
- Provide a list of Frequently Asked Questions, and your contact information (including phone number, email, and physical/mailing address)
How To
Options for building your online store include manually with HTML, manually using a database (although I really don’t recommend it — this may be a good way to learn a bit about PHP and MySQL, but it’s not going to be your best option), or through a shopping cart builder software. 
Your web host probably has a number of easy to install options for creating a store, either directly from your cpanel, or from something like Simple Scripts or Fantastico (if you are lucky enough to have the choice, use Simple Scripts!).

Simple Scripts
If you are considering a specific cart, check around the web for reviews, tutorials, and demos before you actually get started. There are a lot to choose from, and many are either open source, or included with your web hosting. If you do decide to use a shopping cart that you must first purchase, be sure you know what you’re purchasing, and why.
If you are already using Drupal, Joomla, Wordpress, or practically any other common CMS, there’s a good chance there is a shopping cart module. For Drupal, I’ve played with Drupal e-Commerce and Ubercart, and greatly prefer Ubercart. Joomla seems to have more options than I’d care to count, and WordPress has quite a few as well, including WP E-Commerce.
The wonderful thing about using a shopping cart is that the whole process becomes very intuitive. You click here to upload a photo, type in a description and price, set limits and shipping as appropriate, and you’re done! You are responsible for the content, but not the coding. It also makes it very simple to make updates.
Most carts integrate well with a variety of payment processors, so configuring the payment part of the cart is likely to require a little bit of set up when you first build the store, and then you can pretty much forget about it (whereas if you’re building from scratch in HTML, you’ll be spending a lot of time logged in to Paypal building buttons).
Testing!
One important final thing to remember is to check your site in mulitple browsers – both to see how it looks, and how it acts. Microsoft has anti-phishing capabilities built in to Internet Explorer, and I once found out one of my sites was producing a message telling visitors using IE (and paying attention) that it could be a phishing site. I had to correct Microsoft on this a couple of times, so make sure you periodically check this.