Most Open Educational Resources (unless they are in the Public Domain) are licensed for use with a Creative Commons licence. There are six Creative Commons Licenses, the majority of which qualify as OER. The licence will indicate what you can to do with the resource.
The CC BY attribution license lets you freely adapt and use the resource as long as you credit the original author(s) and indicate if any modifications have been made.
The CC BY-SA attribution, share alike licence lets you freely adapt and use the resource as long as you credit the original author(s). Any modifications must be noted and the new work issued under the same licence.
The CC BY-NC attribution, non-commercial, licence lets you freely adapt and use the resource as long as you credit the original author(s), indicate where you have made modifications. You cannot use the work commercially.
The CC BY-NC-SA attribution, non-commercial, share alike licence lets you freely adapt and use the resource as long as you credit the original author(s), indicate where you have made modifications and share the new work under the same license. You cannot use the work commercially.
In addition to materials licensed with a Creative Commons licence, material that is in the public domain can be freely used in your teaching and doesn't even require attribution (although that is always a good idea). Because the terms of copyright vary from country to country, it may not be clear when a resource is in the public domain. Most often it is older works or US government materials that are in the public domain, but you will also find recent materials whose creators have released their work into the public domain.
The Public Domain Mark enables works that are no longer restricted by copyright to be marked as such in a standard and simple way, making them easily discoverable and available to others.
The CC Zero designation indicates that the creator has released their work into the Public Domain and that it is free to use.