First, get a good test kit. Links to the ones we recommend are in my signature. We call them "guess strips" for a reason -- testing with them is no better than guessing.
Next, your pool is a pool, no matter the size. It's liable to the same standards of sanitation as a pool ten times its size. Your pool as pictured isn't sanitary.
And yes, you really can keep it sanitary using bleach, borax and baking soda. We can show you how. First steps first, get a good test kit with FAS-DPD reagents so you can KNOW what your free chlorine FC is.
After you have your test kit, post your results like this
FC
CC
pH
TA
CH
CYA
Then we can give you tailored advice toward SLAMming your pool. For now, add 5 ppm FC to your pool daily, using liquid chlorine. No Clorox, scented, or splashless stuff. Wal-Mart is a good source of everything you'll need to maintain your pool.
You can do this!