There's now a new and easy-to-use in-browser editor, iD; clicking "edit" on the "default" OSM slippy map gets you there by default, and it even has a walk-through for first-time users:
http://www.openstreetmap.org/#map=16/51.5011/-0.0194(As for me, I prefer jOSM - more complex, Java-based, not in-browser; more powerful in various ways: https://josm.openstreetmap.de/wiki/Download )