Let see an example:
1 - Zoom in a region, and select an area of interest with the "Define Area" button. In this example I choose the Vesuvius volcano in Italy.
2 - Just select the "Download Data for Defined Area" button (you need a free account at this step). Now you can select the preferences on the file format.
In this example I selected the ASTER Global DEM database (30m cell), a ArcASCII format (we need a numeric DTM), a projected UTM metric coordinate system. In the field "Research" area you can choose your field of use of these data. When ok select "Submit".
In few seconds a new window with the DTM image preview and the information of previous selected preferences will appear.
Now you can download your DTM!
3 - Once you got your DTM in ArcASCII file format, you have just to modify its header: open the file with a text editor and modify it as follow.
Basically you will use the "cellsize" instead of "dX" and "dY". This step is necessary because Surfer cannot read the file with its original header.
4 - Open Golden Software Surfer and select "Grid"->""Convert" in the menu.
Then select as "ASC Arc/info ASCII Grid" as file type and select the modified file.
Following the convertion procedure you will get a .grd in surfer file format of your DTM.
5 - Enjoy your data with Surfer! Some example reported below. You can use these data as base for your maps or to upload it in the GPS. Remember that you are using a WGS84 - UTM datum.