One of the things that makes wine making so attractive is that you don't have to spend a ton of money to get started, and if you already are buying wine at the store it can actually save you money, after all , you should have plenty of bottles. But there are some basic pieces of equipment you will need before making your first batch.
Of course you will need a container, I have found that plastic works best for fermenting the juice and an air-lock will also need to be able to fit the container. This is to allow gases to escape without letting stuff back into the wine during fermentation like nasty buggies! For siphoning your wine off of the sediment a 1/2 plastic hose works well. All very simple items.
If you are making wine from fresh fruit a straining bag comes in handy. It is used for easy removal of the pulp during fermentation. You can leave the bag in the fermentation, filled with pulp, and simply pull it out at the right time.
A hydrometer will allow you to determine the alcohol level of your wine and it will help you to track the progress of your wine's fermentation. So you will also want to get one, you will find that it is an invaluable tool!
There is a lot of other cool wine making supplies, but these are really the basics to get you on the road to making your first vino! Wine making should be fun so relax and enjoy the experience!