If you have one of the supported Linux distributions, you can follow the steps on the .NET Core website: https://www.microsoft.com/net
If you have an unsupported distribution:
Download the .NET Core SDK from the links, picking the distribution closer to the used one.
https://www.microsoft.com/net/download
If you have support for deb packages, you can install Ubuntu/Debian packages.
If you have support for yum packages, you can install Fedora packages.
Make sure your system has at least:
llvm-3.7.1-r3
libunwind-1.1-r1
icu-57.1
lttng-ust-2.8.1
openssl-1.0.2h-r2
curl-7.49.0