To find some expressions, you need to get creative and potentially use more advanced operations (like square roots, factorials, concatenation etc.), or allow the use of the digits more than once.
Here are a few examples showing how to form *some* numbers using 1, 4, 8, 9 only once with basic operations (note that many numbers are unattainable this way):
* 9 + 1 = 10
* 1 + 9 - 4 - 8 = -2 (negative numbers can be made, but this doesn't help reach 1-100)
* 9 + 8 + 4 - 1 = 20 (This is just an example. Many combinations are possible, but few make numbers in the 1-100 range)
To systematically find expressions, you'd need to use a computer program that explores all possible combinations of the four digits and the arithmetic operators. Even with such a program, the limitations using only four digits and basic operations will prevent the creation of a significant portion of the numbers from 1 to 100.