1. Explain it simply
随着 (suízhe) means 'as' or 'along with', linking one change to another.
Word order: 随着 + background (a noun or short clause) + comma + main clause.
The main clause often uses 越来越 to show it changes step by step: 越来越少, 越来越好.
随着 must sit at the very front - it cannot go between a subject and its verb, or head the result clause.
2. Show examples
随着天气变冷，来公园的人越来越少。
Suízhe tiānqì biàn lěng, lái gōngyuán de rén yuèláiyuè shǎo.
As the weather turns cold, fewer and fewer people come to the park.
随着 heads the whole background
随着时间过去，我们的关系越来越好。
Suízhe shíjiān guòqù, wǒmen de guānxì yuèláiyuè hǎo.
As time passes, our relationship gets better and better.
the main clause changes along with it
随着城市发展，生活越来越方便。
Suízhe chéngshì fāzhǎn, shēnghuó yuèláiyuè fāngbiàn.
As the city develops, life becomes more and more convenient.
越来越 marks the gradual change
3. Share a tip
Keep 随着 at the front - say 随着天气变冷, not 天气随着变冷.