Save the mind map as an Image. Depending on what program you use, it may save automatically. If not, Hit ctrl+Printscrn Buttons. Then go to a program such as Paing (PC) and click ctrl + V. This will paste the picture onto the program. You may then hit "Select" and outline the portion you want to use and then hit the "Crop" key. Save your picture on your machine. You may then upload it to the website of your choice according to their uploading method which normally asks you to "Choose File" and hit "Upload."
Save mind map in Freemind (free program). Export as HTML or Image. If you export as .mm file (their extention), you will need to upload a piece of software from their server to view it. The downside is people you want to see the program must have Freemind as well.
Use an online service which will give you a code to embed (place) the file onto your Website or blog. Some even have links which you can submit to social networks for people to view the mind map. The plus side of this method is there is no need to upload images or software onto your server and if you want people to be able to click to expand the mind map, they will have that ability.