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Unfortunately the only true way to know is to either consult a list or simply memorize major examples in each category. Some basic trends are easy enough to memorize and remember, such as all acids based on halogens are strong (like HF, HCl, HBr, HI) and all organic carboxylic acids are weak (like acetic acid and formic acid). But many other examples simply must be remembered. For example, nitric acid (HNO3) is a strong acid but ammonia (NH3) is a weak base.
One thing to keep in mind, however, is that the conjugate base of a strong acid is a weak base. Take the example below:
HCl --> H(+) + Cl(-)
HCl is a strong acid so it will ionize completely in water. But its conjugate base Cl(-) is a weak base. So when you dissolve NaCl in water you know that the Cl(-) produced will not act as a strong base.
This is usually done by the litmus paper test, it basically tells you if the chemical is acidic or basic. if the PH level is between 0-7, it is considered acidic, the closer it gets to 0, the more acidic it is, whereas from 7-14 is basic, the closer it gets to 14, the more basic the substance is.
We define a strong acid, an acid which easily gives up it's proton, the proton possess a weak bound. We define a weak acid, an acid which hardly gives up it's proton, the proton possess a strong bound.
Strong bases are fully ionized in cations and hydroxyl ions, while weak bases (eg. NH3) react, only to a small extent, with the proton yielded by water. Therefore, their solution contains only a low concentration of hydroxyl ions.
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