How can I convert this pixelated soil map raster in to a normal smooth continuous map? Since I am new to this, it would help if the explanation is step by step. Thank you.
That is the 'normal' appearance. Rasters are made of square cells, hence they are 'blocky' along the edges at a particular zoom level.
If you wanted to have it less pixelated at that zoom level, you could have chosen a much smaller cell size in whatever process that you used to create it.
Doing anything else to the raster will change things... is this just for appearances sake?
I have extracted the data from it but I want to put it in a report. I was checking some other maps and they were not blocky so I thought mine has some issue. I asked one of my seniors about it and he told me to convert the raster into vector, do some modifications and then convert it back into raster to remove the blocky edges.
Raster to Polygon—Conversion toolbox | ArcGIS Desktop with generalize option to get rid of the choppies
Then there is no need to convert back to raster for a report, just use a screen grab of the vector and save as *.png.
If you need a *.tif, then use a really small cell size