InDesign will not let you edit images (thankfully). For parts of the image to be transparent the image file will have to contain transparency (to put it simply).
Now, there are a few options here (you did not provide enough detail).
1. If your logo is in a vector format (ai/pdf/eps) it _might_ contain transparency but it doesn't show up in the low-quality thumbnail/preview in InDesign. To check this, right-click the image and set Display Performance to High Quality. If it's still not transparent, open it up in Illustrator and remove the background there.
2. If your logo is a jpeg, then you possess a low-quality copy of the logo created by amateurs and I recommend you acquire the original. If it's all you have then you should save it as PSD (or TIF with LZW and Transparency) and make the transparency in Photoshop (use a layer mask, or add a clipping path).
Note: If you have transparency in the placed image file, but it doesn't seem transparent in InDesign make sure you have not filled the box with a white fill color in InDesign. It should be set as "none" (the "color" looks like a white box with a red line through it).
Ps: InDesign does have an option to create an automatic clipping path around your image, but this is highly inaccurate and is only recommended for fast mockups. I'm mentioning it just in case someone suggests it.