Christianity emerged from Judaism, which itself rejected figurative religious art as being too much like idol worship (see Ex 20:3). But once Christianity became the official religion of the Roman Empire under Constantine in the 4th century CE, it was not long before Roman practices of portraying and honoring the divine (their gods and emperors) would make their way into Christian practices as well.
Although the saints are portrayed in statues, icons, paintings, and other media, they are not worshipped as God is. Rather, we venerate the saints, meaning that we honor them, give them respect, and show them devotion for what they have accomplished in their lives of faith. John Coleman, SJ sees saints as generally having five characteristics:
exemplary model
extraordinary teacher
worker of wonders or source of benevolent power
intercessor
possessor of a special, revelatory relation to the holy.
In short, they invite to see and relate to God anew.
Asking saints to intercede for us is not idol worship because they themselves are not the object of worship. We are asking for their help to make our case before God, just as you might have a friend advocate for you.