Welcome to the PF, Karl.
First, I have to caution you about working with AC mains voltages like 230Vrms or 120Vrms. This is very dangerous stuff, and if you don't know what you are doing, you could easily hurt or kill yourself, and it is easy to build something that catches fire.
Now, keeping that warning in mind, I recommend that you find a good book on electronic prototype construction, and read the parts about electrical safety and about product construction to meet safety regulations (like Underwriter's Labs here in the US). Those are fundamental issues that you will need to keep in mind as you start building projects that connect to the AC mains. Honestly, beyond the shock risk to you as you build the project, if you don't do several things correctly in the construction of your device, you may end up shocking some other unsuspecting person, or catching your house on fire some day down the road when the device fails for whatever reason.
Okay, I googled power supply construction tutorial, and got lots of good hits. Here's one example:
http://my.integritynet.com.au/purdic/power1.html
And to answer your question, Yes, you will need a smoothing capacitor after your full-wave bridge rectifier. The size of the cap depends on your output current requirements, and how much ripple you can withstand on the output. BTW, why does the link that I gave above use an isolation transformer between the AC mains input and the rectified output? It's an important Quiz Question!
For a better DC output, you would put a linear regulator circuit between the rippling DC output on the bridge output cap, and your DC load.
Stay safe, and please check out your local technical bookstore (or Amazon.com) for a good book on electronic prototype construction.
