Many mods are inherently incompatible. This doesn't mean that they don't work together though, as they might edit the same thing but the scope of one mod might be different. You can make one mod overwrite another by adjusting your load order, or you can make a patch, merging the changes the plugins make. There are a lots of patches available, and sorting LOOT will give you a good base for your load order, but unfortunately for larger load orders this simply isn't enough.
Load Order is extremely important while patching. When you make a patch for a mod or a group of mods, you want the patch to load after said mod(s). Some patches which patch the entire load order require themselves to be at last position, and require re-patching every time load order is changed or a new mod is installer. For more on load order in patching, see Load Order page.
Wrye Bash
Wrye Bash was originally used to manage and install mods. Wrye Bash can generate patches (called Bashed Patches), that can sort leveled lists, tweak actors/NPCs, tweak in-game things that are otherwise almost untweakable such as cell respawn time,bounties for crimes etc, and manage quite a few other things. Here is a video guide for it. This can be used in conjunction with other patching methods.
Synthesis
Synthesis is a patching tool used to create advanced custom patches that do various things with just a few clicks. This is the modern automated patching replacer. It has many, many patches. You can browse through it's repository here or inside the application. Here is a basic video tutorial for Synthesis. Additionally, there is an experimental patcher known as Synthesis Fusion that patches ALL records, including leveled list. It takes longer time based on how many plugins you have active. You can find the patcher in the in-app repository too. However, it is known to not work for some users. Make sure you are using a separate master synthesis for it alone. You can add a separate master by clicking on the + icon, and you can drag patchers to them.
Creating patches by hand is known as manual patching. Tools such as xEdit is essential in the creation of manual patches. Do not attempt to create manual patches if you don't know what you are doing, as it can cause bugs if done incorrectly. However, it is sometimes necessary to create manual patches to properly resolve conflicts.
See The Method for an example of Manual Patching and more on this.