How is the process of finding equivalent ratios like the process of finding equivalent fractions?

It's generally the same, because each ratio can be written as a fraction and each fraction can be written as a ratio. For example:

1 : 2 = 1/2
5 : 7 = 5/7
3.5 : 4.3 = 3.5/4.3 = 35/43
etc.

Finding equivalent ratios is just multiplying or dividing both sides by the same number. Finding equivalent fractions is multiplying or dividing both numerator and denominator by the same number, so it's the same. For example:

1 : 2 = 2 : 4
1/2 = 2/4

5 : 7 = 10 : 14
5/7 = 10/14

3.5 : 4.3 = 7 : 8.6
35/43 = 70/86

etc.