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Illustrator has a yellow icon that says "Ai".  Click the icon on your PC or Mac to open Adobe Illustrator. If you don't have a subscription to Adobe Illustrator, you can use Inkscape which is a free and open-source alternative to Adobe Illustrator.  It has many of the same features that Adobe Illustrator has. Use the following steps to create a new file in Adobe Illustrator.  Click File in the menu bar at the top. Click New. Type a name for the file next to "Name". Click Ok. Having rulers on will allow you to add guides to your artboard. You can drag a guide onto the artboard by clicking and dragging the ruler on the left or top.  Use the following steps to turn on rulers.  Click View in the menu bar at the top. Hover over Rulers. Click Show Rulers. The Artboard Tool has an icon that resembles a square with crop marks in the corners.  It's in the toolbar to the left.  Click this icon and then click and drag the edges of the white artboard in the center of the screen to adjust the size of the artboard. Most logos are designed on a vertical rectangle-shaped artboard or an even square-shaped artboard.  A rectangle-shaped logo will look good on banners, signs, and a social media cover page, but a square-shaped logo will fit into more media platforms, such as the corner of a business card or a social media profile icon. It's in the menu bar at the top of the page. It's in the File menu.  This saves your file.  You should save often while working.
Open Illustrator. Create a new file. Turn on Rulers. Adjust the artboard to fit your logo idea. Click File. Click Save.