How to make a PDF smaller
Shrink a PDF with PDF by Zaweba: Reduce file size in one click, or choose a preset, picture resolution and JPEG quality, and do several files at once.

One click on File, Reduce file size in PDF by Zaweba makes a PDF smaller. If you want more control, open its settings to choose a preset (Balanced, Smallest file or High quality), set the picture resolution and JPEG quality, and pick from 15 things to discard or flatten. You can also shrink several files at once into a folder, leaving the originals untouched. The app is free and works offline on Windows.
Big PDFs are usually big because of pictures, so most of the saving comes from them.
The one-click way
Open the document and choose File, Reduce file size. Save the result under a new name and compare the sizes. For many files, especially ones exported with full-resolution photos, that's all you'll need.
Using the settings
The presets are a sensible place to start. Balanced aims for a good saving while keeping pictures looking right on screen and in ordinary printing. Smallest file squeezes harder, which suits email attachments and upload forms with a size limit, at some cost to picture quality. High quality makes a smaller saving and keeps pictures close to the original, which suits documents going to print.
Picture resolution sets how much detail pictures keep. Photos taken on a phone are often far more detailed than a page needs. JPEG quality sets how hard photos are compressed; lower gives smaller files but can show blocky edges, so check a page or two at full zoom.
The list of things to discard or flatten lets you drop parts of the file you don't need. Pick only what you're sure about.
Finding what's taking the space
If a file stays stubbornly large, use Audit space usage from the same menu. It shows bytes by kind, so you can see whether pictures, fonts or something else is responsible. A large share for pictures tells you to lower resolution; a surprise elsewhere tells you where to look next.
Doing a batch
Reduce file size can work on several files at once and write the results into a folder, leaving the originals untouched. That suits a folder of scanned documents before archiving. Tools, Actions has a reduce size step too, and a built-in action called Optimise scanned documents.
Saving habits that help
Ordinary saves are incremental, adding changed objects to the end of the file, so a document edited many times can grow. Save as leaves out unused objects and can pack small objects into compressed streams, so it often gives a smaller file by itself. Removing hidden information, such as earlier versions and attached files, can also free space.
Keep the original
Don't overwrite the original. Once picture detail is thrown away, it doesn't come back. Keep the full file for printing and editing, and make small copies for sending.
Don't shrink a document that's going to a professional printer without checking with them; they usually want full-resolution pictures.
PDF by Zaweba does all of this on your own PC, so you don't need to upload private documents to an online compressor.