If you've already installed one or more .NET SDK versions via the package manager, uninstall them before proceeding.

Download the SDK versions you want to install from here. For this example, I'll be installing .NET 8 and .NET 10, downloaded as dotnet-sdk-8.0.416-linux-x64.tar.gz and dotnet-sdk-10.0.100-linux-x64.tar.gz, respectively.

Open a terminal.

If ~/.dotnet already exists (from a previous installation), remove it:

rm -rf ~/.dotnet

Create a new, empty .dotnet directory:

mkdir ~/.dotnet

Extract the SDK archive(s) into the .dotnet directory:

tar zxf dotnet-sdk-8.0.416-linux-x64.tar.gz -C ~/.dotnet/
tar zxf dotnet-sdk-10.0.100-linux-x64.tar.gz -C ~/.dotnet/

Add to .profile:

export DOTNET_ROOT=$HOME/.dotnet
 
export PATH=$PATH:$DOTNET_ROOT:$DOTNET_ROOT/tools

Restart to apply the new .profile settings.

Open a new terminal and verify that the dotnet CLI is working correctly:

dotnet --list-sdks

You should see something like this:

8.0.416 [/home/username/.dotnet/sdk]
10.0.100 [/home/username/.dotnet/sdk]

Taken from here: https://learn.microsoft.com/en-us/dotnet/core/install/linux-scripted-manual#manual-install