There are two ways. The first, currently experimental, allows you to run locally. Don't do this for production:

pip install ton-http-api
source ~/.bash_profile
ton-http-api

The second is through Docker:

mkdir private
curl -sL https://ton-blockchain.github.io/global.config.json > private/mainnet.json
curl -sL https://ton-blockchain.github.io/testnet-global.config.json > private/testnet.json
./configure.py
docker-compose build
docker-compose up -d

You can see the entirety of the instructions on the TonCenter GitHub repository.