ETA: 99.9% of machine embroidery software runs on Windows only.
You really need nothing to access or download design files from the Internet.
However, you do need software such as PED Basic or Magic Box or the Amazing Box. These are reader/writer units that require a rewritable memory card in the format of the embroidery machine.
For the ESL, the format is pes, which what PED is designed for. For any other product, you need to make sure the card is the pes format.
Now, for actually seeing the design files before sending them to the reader/writer/memory card, or composing words, you will need a software program such as Embird.
The beauty of Embird is that you start with the basic program and then add additional functions that work off the basic program as you progress in learning machine embroidery software.
You should be able to get PED for around $100 - http://www.allbrands.com/products/abp01060.html make sure the card is not limited to the 4 x 4 hoop. Embird starts at $131 and you can download a trial program here - http://www.secretsof.com/content/1853
In the meantime, you can start compiling a folder for downloads without any software. Create a folder and name it Machine Embroidery Downloads. Save downloads to this folder so they can be easily found.
Downloaded files are usually zipped/compacted for faster download time. The file has to be unzipped or extracted and the unzipped/extracted file is what you save and use.
As you find designs you like, make sure they are in the correct format and size. Embroidery machines are limited to what size design they can stitch out. For example, if the largest area is 5 x 7, a larger hoop will not enable the machine to stitch out any larger than the limitation of the machine.