How to copy a design into Word or PowerPoint with transparency
Copy in Vectornation by Zaweba puts PNG, EMF and PDF on the clipboard, so artwork pastes into Word or PowerPoint with a clear, transparent background.

Select the artwork in Vectornation by Zaweba and press Ctrl+C. Edit > Copy puts the selection on the clipboard as a PNG, an EMF and a PDF at the same time, so when you paste into Word or PowerPoint the program takes the format it likes best and the background stays clear rather than turning into a white box.
The white box is the common complaint. Many graphics programs copy only a flat bitmap, and Office pastes it with a solid background that hides whatever is behind it. Putting several formats on the clipboard at once avoids that.
Why three formats
Each format suits a different kind of paste. PNG is a picture made of pixels that keeps transparency, which nearly every Windows program understands. EMF is Windows' own vector picture format, which Office applications handle well and which stays sharp when you resize it. PDF is there for programs that prefer it. You do not have to choose; the program you paste into picks.
Copying and pasting
Select what you want to copy. A whole logo is best grouped first so you get everything in one go.
Press Ctrl+C or use Edit > Copy.
Switch to Word or PowerPoint and paste. If you want to control which format arrives, use the program's paste special option and pick the one you prefer.
Resize the pasted artwork with a corner handle so it keeps its proportions.
Making the paste look right
Check the result against a coloured slide background, not just white. That is the quickest way to see whether the background really is transparent.
Keep the original drawing. Once a logo is in a slide, edits are easiest made back in Vectornation and pasted again, rather than trying to fix it in the presentation.
Think about size before you copy. A large, detailed illustration pasted as a picture can make a document heavy, so for a small logo in a letterhead it is often enough to copy just the logo rather than the whole artboard.
If the slide or page has a coloured background, choose colours in Vectornation that still read against it. A dark logo on a dark slide will be transparent and invisible at the same time, so keep a light version of the artwork ready for that case.
For documents that will be shared widely, consider whether the people opening them have the same fonts. If your artwork contains text, and you cannot be sure, make an outlined copy of the text before copying, and keep the live version for later edits.
Going the other way
Paste works into Vectornation too. Images pasted from other apps keep their transparency, and SVG copied from other apps pastes as vectors, so you can bring a graphic from a web tool or another editor straight onto the canvas as editable shapes.
When a file is better than the clipboard
For a document template or a presentation you will reuse, a saved file is easier to manage than repeated pasting. File > Export writes PNG, JPEG, WebP, TIFF, BMP and GIF with settings for background and resolution, and Vectornation also saves EMF and WMF, so you can insert the same graphic into many documents from one place. Asset export can write several formats of the same artwork in one go when you need a set.
Vectornation by Zaweba is free software for Windows, works offline and needs no account.