The black screen is when you start up Minecraft, login and never get to progress to the main menu. There are a ton of reasons why a black screen can occur, but here are the most common:
Has Minecraft updated recently?
If Minecraft has updated recently, most likely mods will be broken. Check the Minecraft forums to see if your mods have been updated to the latest version. If Minecraft has been updated, check the Minecrafter website and/or thread for updates. You should always update to the latest version of Minecrafter.
HD Fix incompatibility
In the off chance that your mod is still compatible with the update, then the HD fix may be causing the problem. Try disabling custom water & lava first (via the options tab). If that still doesn’t work, try disabling the whole HD fix altogether.
If you have to disable the entire HD fix, then make sure you don’t have any texture packs in your mod package larger than 32×32. Only texture packs 16×16 & 32×32 can be loaded into Minecraft without the HD Fix (although 32×32 textures will have the dreaded fire bug on certain blocks). Anything higher requires the HD fix and will black screen without it.
Although Minecrafter works with any minecraft.jar, any mods you’ve installed manually before using Minecrafter may be causing an issue. Delete your bin folder and start up Minecraft to begin re-downloading the files. Then, try Minecrafter again.