Construct a table with two columns, for x-values and y-values.
Choose x-values to plug into the function. These x-values must be close to the number for which you want the limit. For instance, if you want the limit of y=1/(x+1) as x approaches 2, then you could plug in 1.7, 1.8, 1.85, 1.9, 1.95, 1.96, 1.97, 1.98, 1.99, etc. If you want the limit of the same function as x approaches infinity, then just plug in increasingly large numbers: 100, 1000, 10000, 100000, 1000000, etc.
Notice any tendencies that emerge as you plug in numbers that are increasingly close to the value in question. Here, as x values get closer and closer to 2, the value of the function approaches 1/3. As x values get closer and closer to infinity, the denominator gets larger, and the function gets more minuscule, approaching 0. Thus, the limit as x approaches 2 is 1/3 and the limit as x approaches infinity is 0.