Summarize:

You will need a good microphone and a way to prevent echo or background noise from bleeding into the sound you want to keep.  A high-quality computer microphone will work effectively enough for a beginning cartoon, but if you plan to seriously market and distribute your cartoon, you will eventually need to invest in more professional equipment. When working with a small microphone, encase it in a tube speaker box lined with foam to cut out echo and excess background noise. Get creative and look for simple, everyday ways to make noises passably similar to the noises you need for your cartoon.  Make a list of sound effects you will need. Be creative and thorough, including everything from the obvious (explosions, alarm clocks) to the less obvious (footsteps, background noise).  Record different versions of each sound so that you have more options to use. A few examples of sounds you can create include: Fire - Manipulate a piece of stiff cellophane Slap - Clap your hands together once Thunder - Shake a piece of plexi-glass or thick cardstock Boiling water - Blow air into a glass of water using a straw Baseball bat hitting a ball - Snap a wooden matchstick If you do not have access to the equipment or otherwise find it impossible to make your own, there are CD-ROMS and websites offering royalty-free pre-record sounds you can use as desired, and this might be a more viable option for you. Always review the usage permissions for any pre-recorded sound effects you use. Even if something is free to download, it may not be free to use, especially for commercial purposes. It is very important that you know what you are permitted to do before you use a sound for your cartoon. If your cartoon has dialog in it, you or others you know will need to be the voice bringing your characters to life. As you record your lines, read from the script using appropriate intonation and expression, and make sure that you match your lips to the animated lips of the cartoon. Consider manipulating the voices using computer software. If you have fewer voice actors than characters, you can change the voice of one character simply by adjusting the attributes of the voice sample you already gathered. You will need to invest in special audio editing software to do this, but depending on which one you use, you can likely change the pitch and add overtones, like metallic garbles, to the voice recording.
Get the right equipment. Record your own sound effects. Look for free pre-recorded sound effects. Record real voices, if necessary.