There are a number of way in which one can determine whether a liquid is an acid or a base. The laboratory method would be to simply measure its pH, a value above 7 indicates a base and value less than 7 confirms an acid.
At school level, esp. during an introductory chemistry course, we can use either litmus paper or red cabbage juice. The acid/base determination is based on the color. Here are the steps for litmus paper based test:
1) Pour the liquid to be tested in a small bowl or glass.
2) Dip a piece of red litmus paper in it and note the color change. Repeat the process with a piece of blue litmus paper.
If, the red litmus turns blue and blue litmus remains unchanged, liquid is a base.
If, the blue litmus turns red and red litmus stays unchanged, liquid is an acid.
If, neither the red nor the blue litmus paper changes color, it is a neutral liquid.
Red cabbage juice can also be used and students can add few drops of the liquid in a tablespoon full of red cabbage juice and observe its color. If the juice turns red, liquid is an acid; if juice turns blue (or green), liquid is a base.
Hope this helps.