I am not an expert in flooring or flooring tools, but I may have some information to help you find more information.
Option#1: You can look up videos, like on YouTube, about becoming a Flooring Installer. You may notice that depending on the type of flooring, climate, location, and materials used, your equipment and tools will always vary.
Option 2: Many employers and schools (like community colleges) may have some type of apprenticeship program for installers or masonry programs (which may cover flooring). These programs could be 3 months to 1 year but you will be learning practical skills that you can apply right away and have a expert mentor along the way. Be sure to look for programs that offer many levels of training, cover your costs, and prepare you for a job right after the program.
By participating in an apprenticeship or formal training program, you may find that you have better access to bigger jobs with corporate organizations, developers, or larger firms because you are certified and properly licensed to do this work.
If you want an actual certificate or license, please be careful to check if these schools or programs are accredited by the US Department of Education (or ask a college advisor or college librarian at a nearby college to check it for you).
I hope this helps as you continue to search for answers.
Most installers will have a specialty trade, such as someone who does Tile floors and walls usually only do that, as there are fewer tile installers and it's a little dirtier and less forgiving of mistakes. It requires a tile saw and grout tools like trowels and grout pan/buckets. There are several common types of tile used, and each will have a slightly different way of laying and patterns of installation. They are all set in thin-set concrete/grout, laid using spacers and then left until firmly attached and then the interlocking grout is installed. There is a trick to the installation of this, which usually comes with experience and your ability to use that small tool set.
Real wood flooring installers may also do carpet/laminate, there are many more of these trades people. The tools for real wood flooring would include hammers, prybars, cut nails, floor sanders, rollers and paint brushes. They will also know staining and urethane installation methods, as they always should be sealed and protected after installation. There is also a prep phase with wood flooring in that it needs to acclimate to the location it's being installed in for at least 24 hours, out of the plastic in order to adjust to the room normal humidity and temperature.
Carpeting, laminate and even VCT (Vinyl Tile) are relatively common. The all require similar tools, except that carpeting installers seem to have special knee pads in order to "shove" the carpet to stretch it into place at the edges to get it attached down on the carpet tack strip. Hammer, finish nails, cutting and measuring tools. VCT is always glued down, which is a similar process to the tile thin-set, where you'll need applicators for that.
Which flooring type to pursue? It may be best to look at what's used more widely in your area and what's more rarely used. I'd assume in El Paso, Tile is prominent in housing and commercial buildings and would be a place to start.
Mary recommends the following next steps: