I just recently purchased a Blue Snowball USB microphone and a Dragonpad Studio Mic Filter pad because I am interested in creating videos and podcasts. However, I am still experiencing excess background noise. Is there any way to reduce this using Audacity or any other freely available program?
I'm not sure if Audacity has this, but what you need is a compressor (actually an expander, but they're opposite things built into a tool referred to as a compressor). The compressor allows you to limit sound that is above a certain dB level, the expander limits sound under that level, called a gate. You can set a gate with the compressor at a sound level, cutting out faint background noise but keeping your voice. This will also cut out breathing noises you make at the beginning and end of syllables particularly Hs and Ss. This technique will not work if your voice is not considerably above the level of the background noise.
Another tool which can help refine your voice, but not entirely solve the noise problem is an eq (equalizer). Look specifically for a parametric eq; these are the most intuitive. Essentially the equalizer loudens or softens sound based on its frequency. You can use this to raise the level of your voice, but also soften background noise. This works particularly well if there's a hissing sound that fills up only a small area on the frequency spectrum.
In terms of the recording environment, ideally you could build a sound proof room, but these are incredibly expensive. Another slightly cheaper idea is to give your recording room an acoustic treatment, essentially coating the walls in acoustic foam. This won't solve existing noise problems, but it will limit reverb. Acoustic treatment is fairly cheap. Generally you can coat a fairly large room at 50-75% coverage for under $100.
UPDATE: Audacity does have a compressor, but the GUI looks really ugly and unintuitive. A parametric eq also requires an external plugin. That said, it's still probably the best free program available. Something paid and marketed as a DAW (digital audio workstation), would do the job much better. Something like Adobe Audition, Apple Logic Pro, or Avid Pro Tools.
Audacity has a compressor effect, however I found the "Compress dynamics" VST plugin generating better results, see more here. If you want better control over the compression parameters you should try SoX.
Another approach is to try the Vocal Remover VST plugin for Audacity (it is in the same package as Compress dynamics), and if it succeeds in removing the vocals then you can run the result through an inverter (in the VST pack too) and apply it to the original track.
You may find this answer from our sister site Sound Design to be useful. Basically, it depends on the kind of noise you are getting though. If it is random background noise, then it may be fairly difficult to remove unless it is pretty regular frequencies. Either way, most noise removal tools will listen to the noise and try to identify what they can remove.
Your best bet is to prevent noise from occurring in the first place. There are two main ways to do this, decreasing the noise itself and increasing the signal (and using less gain if needed).
For reducing the noise, your options are limited if the mic itself is noisy, however if there is any background noise in the room you are recording in (such as fans, power supplies, air conditioning or heating, etc) turning them off or recording in a quieter location will help considerably.
For increasing signal, get closer to the mic. Make sure the mic has its gain set such that it is getting the strongest possible signal without cliping (maxing out the volume it can record). This will result in a signal that is as strong as possible and keep the noise floor as low as possible.