Illustrator background of objects (lasso and magic wand issues)

Hello Forum.

How do you make the background of an object transparent in Adobe Illustrator?

I have been having issues with using the Magic Wand tool in Adobe Illustrator as well as the lasso tool.

Basically, I am trying to put a small graphic into a new Illustrator file.

The first thing I tried to do is to use the magic wand tool. But I found out that this did not work on a jpeg image since it did not have any individual objects to select.

So I tried something new. I opened the file in Adobe Photoshop and used the lasso tool to select an area. Then I coped this area. Then I tried to paste it into Adobe Illustrator. But the background was not transparent for the pasted image.

Try saving it first as a transparent png file?