Installation of OSM on Garmin GPSmap 62stc

The general procedure is as follows:

1. Go to the list of available maps and choose one that suits you
2. On the download site, follow whatever instructions the site owner / map maker gives to select and download your map
3. Once downloaded, you should have a file called similar to "gmapsupp.zip" (maybe with more detail like date or kind of map in the name). Unzip that file by whatever means your operating system offers (probably a right-click and 'Extract').
4. You should now have a rather big file called "gmapsupp.img". Transfer this to the Garmins internal storage or (better) to the SD-card and put it in a folder called "Garmin", (e.g. G:\Garmin\gmapsupp.img). Using the Garmin-supplied USB-cable will work, but removing the SD card and using a dedicated card-reader will be much faster.
5. On a GPSmap62, only one map at a time is supported, so you should see the new map right away (if the map has data in the area where you currently are). On newer devices, you may have several maps at the same time. You can chose which one to see in Settings->Maps on the Garmin. For those newer devices, you are allowed to rename the "gmapsupp.img" so you can have multiple maps in the same folder. (But you have to keep the ".img")

For further help you need to answer the questions already posted as a comment under your questions so we can get a more detailed picture of your problem.

You can check if you have correctly installed the map and then select it. You may also select what level of detail is shown. see pages 12/13 of the user guide see this bit of it: