The cheapest way is to bring it in to a repair shop and have it replaced.
The way that would seem cheapest (but is more expensive than a new phone, usually) is to buy a screen on eBay and replace it yourself. Unless you've done about a dozen of them (techs train on defunct phones) you're going to break something. When you go to fix that you'll break something else. When you finally give up and bring it in for repair (if you can find a shop that will even attempt to repair a phone that you've been working inside), they'll tell you that you pay them for the diagnosis of what's wrong whether you decide to get it fixed or not, and you pay for the diagnosis by the hour, so the longer it takes them to find all the damage you did, the more it costs. The diagnosis can cost as much as replacing the phone. Then you pay for the repair. And if they missed anything (they won't guarantee anything but the repairs they actually do), you'll need the phone repaired again in a few months.
Which is why very few shops will try to repair a phone you've already worked on.