First, cut a few slashes through the leftover wax.
Then, pour boiling water into the vessel. The water will melt the wax, hopefully getting in between the slashes or cracks you added. The melted wax will rise to the surface and float on top of the water.
Once it’s cool enough to handle, remove the waxy top and discard. You may need to repeat this step again if there is still more wax to remove.
Some candle brands will have a sticky glue that holds the metal bottoms of the wicks to the vessel (and some don’t). If your candle has this, you will need to scrape it up with the blunt end of a butter knife or a flathead screwdriver. If the glue persists, you may also need to use soap to remove, or if it’s really persistent you can use a product like Goof Off.
Once all the wax and adhesive is removed, clean the vessel well.