1. Try a different gridding method. Some gridding methods require more memory than others. For example, Triangulation with Linear Interpolation requires up to four times the amount of memory as Kriging.
2. You may be able to change the search options to reduce memory requirements. The default search of 64 points from four quadrants may be more points than needed. We've had good luck with as little as 2 points per quadrant.
3. Reboot the computer. Surfer requires a contiguous block of memory for operations, so some operations may fail if memory has become fragmented into smaller blocks. I suggest rebooting the computer, closing down all other applications that start during boot up, and then gridding the data.
4. Click File | Options and on the General page, set the Undo Levels to 0. This will not allow you to undo any operation, but may free up some memory. Once you grid the data, you can set the Undo Levels back to a higher number.
5. Open the data file in the Surfer worksheet. Highlight all the data and click Data | Data | Sort and sort the data first on X and then Y values. Re-save the data and close the worksheet. Sorting the data prior to gridding saves memory when opening the data for gridding.
6. Divide the data into smaller files. Grid each file separately and then combine the grid files using Grids | Resize | Mosaic into a single grid file.
7. Try the 64-bit version of Surfer on a 64-bit operating system. The 64-bit version allows for more memory to be available for Surfer. 

See also:

Troubleshooting the "Out of (Global) Memory" error when importing/saving/exporting from Surfer

Updated November, 2021