Why is a logo so important?
A logo is usually someone's first impression into your product and brand. A logo can convey things about your brand or brand reputation.
Before starting to work on a logo design, your team will want to have a finalized product name that everyone is happy with. You should take a look at other logos in the product category/industry that your product is in to get some ideas of various design features of these logos.
A great example of the logo design process is illustrated here. You may find it helpful to look at this example before starting.
The logos below, for example are all from the small appliance/kitchen accessory brands. You can see that there are 3 trends in these logos- all black, red or red/black, and colors with a cool tone.
How to create a product logo.
Looking at the other logos in your product sector can give you a good idea of what to try with your logo. The first thing to do once you have an idea of what you want your logo to look like is to find the right font.
The video below shows how to customize a font. You can start by creating a text box and typing the text of your logo. You can add a stroke to your font to outline in it in a different color or just to make the font thicker. You can change the position of individual characters within the text box. However, a easier way to move the letters around in a logo is to select the text box and right click on it. From there, choose the 'Create Outlines' option and Illustrator will convert the text into a drawing like something you could create with the pen tool. From there, you can move around letters or even alter the way the font looks.