You can add product variations/options by doing the following:

On the Add/Edit Product page, in the Product Data section, click the Add Options tab.
The tab is underneath the shipping tab and has a "spanner" icon.

You can then add product options by clicking the Add Field button. You can add multiple fields as required.
For each field you can add a dropdown menu for colours, sizes etc, checkboxes for options such as giftwap and text boxes where customers can enter personalisation text.

The option prices work as follows:

When you list an item you add the item main base price.

Then when adding options you can add an extra charge for an option which then gets added onto the main base price. If you select Flat Fee the extra fee will be added once and if you select Quantity Based it will be added per item.

If you are selling an item where each option doesn't change the price then you would just add your main base price and leave the option prices empty.