How I can offer customers a discount on one product if they purchase another one?

Create copies of those products which you want to provide with discounts.
Herewith you should initially set lower prices for them depending on the discount which you want to offer.
After that you need to create offers on Offers page and select target products. If target products are bought, additional products will be offered with discount. Or you can leave targets section empty in case if you want to offer extra products with discount for any bought product. And the products with discounted prices for which copies were created should be selected as upsell products.
The way how to hide products offered as upsell from the whole list of products for sale in web store is described here.

Create copies of those products which you want to provide with discounts.