Tools
Tool Training: Similar to other equipment, tools now only work through Training. Features that previously gave Proficiency with a set of tools now gives Training with those tools instead. When you are using tools you are not trained with, you roll the ability check with Disadvantage. When a feature previously required Proficiency with a set of tools, it requires Training instead now.
Using Tools: Tools are only used as a part of an ability check, usually with a skill check. The used skill determines whether the Proficiency Bonus is added to the roll or not.
Tools as Requirements: Some ability checks require the use of tools to be rolled at all. For example, it is not possible to use the Craft options of a set of tools without using the tools and having Training with those tools.
Improvised Tools: When you don't have the necessary tools on hand, you may use objects similar to the required tools instead. In that case, you roll the ability check with Disadvantage even if you are trained with the tools they replace.
Surgery Tools
Surgery Tools are a type of Artisan's Tools that are used in Surgery. Cost: 30 GP. Ability: Intelligence. Skill: Sleight of Hand or Medicine (your choice). Weight: 4 lb. Utilize: Treat disabled body part, as described here.