The most common culprit is a corrupted cache. Open Settings → Apps → Google Play Store → Storage, clear cache and data, then restart the device. If the download stalls at 0% or freezes mid-way, check that you have enough free storage — Android needs extra headroom beyond the app's actual size to unpack it.
If your card gets declined, first verify the billing address matches what your bank has on file. Try removing the payment method and adding it again. Sometimes the issue is a temporary authorization hold — wait 10–15 minutes and retry. If the error code is 'DF-DFERH-01' or similar, clearing the Play Store and Google Play Services cache usually fixes it.
This one is almost always a DNS or account sync issue, not the connection itself. Toggle airplane mode on and off, then open Play Store again. If it persists, go to Settings → Accounts → Google and tap 'Sync now'. On some devices, setting DNS to 8.8.8.8 manually in Wi-Fi settings resolves the handshake error with Google servers.
Sign in to play.google.com and check your order history. If the purchase shows there but the app is gone from your device, it may have been removed from the store — you can still reinstall it from the library page directly. If it's not in order history at all, contact support with your payment confirmation email.
Outdated versions of Google Play Services are usually to blame. Go to Settings → Apps → Google Play Services and check the version — it should update automatically, but you can force it by tapping the three-dot menu and selecting Uninstall updates, letting it reinstall fresh. Also clear the Dalvik cache if you have access to recovery mode.