Just my way...

1. Put the bicycle on a stand or arrange to have the rear wheel clear of ground.
2. Remove rear chaincase inspection cover.
3. Remove front chaincase inspection cover (chainring cover). You don't need to remove the pedal, but it's neater if you do.
4. If your bicycle has rod brakes, remove both rear brake pads.
5. Unhitch gear cable. Loosen both axle nuts and chain tensioner nuts.
6. Rotate crank/wheel very slowly to locate master link over sprocket. Remove master link. Chain will fall, remove it with a hooked wire.
7. It's not a bad idea to clean the bottom of the chaincase with a solvent soaked rag and a stiff piece of wire.
8. Count the links on the old chain and cut new chain.
9. Insert a piece of stiff hooked wire from the front into the top chaincase tube until it exits at the rear. Hitch new chain on hook. Retrieve chain and remove hook. Don't put chain over chainring yet.
10. Insert hooked wire from the rear into the lower chaincase tube. Hitch chain and retrieve it. Install master link and put chain over sprocket.
11. Now, with the wheel all the way forward, the chain should be slack enough to put it on the chainring.
12. Adjust chain tension and reassemble all.

Note that you don't need to take out the wheel to replace the chain this way.