Quick How-to Setup Parity for Ethereum Development (Linux)

0. You can try to install Parity with this command:

bash <(curl https://get.parity.io -Lk)

and go directly to step. 4.
I personally prefer the way described in steps 1-3.

1. To install gdebi package installer, type in terminal:

sudo apt-get install gdebi

2. Download Parity. For Ubuntu and other Debian based distributions use the .deb package. I've downloaded parity_1.8.2_amd64.deb

3. To install Parity:

sudo gdebi ~/Downloads/parity_1.8.2_amd64.deb

4. To run Parity with local blockchain:

parity --chain dev

You should see something like that:

        2017-10-28 22:57:49  Starting Parity/v1.8.2-beta-1b6588c-20171025/x86_64-linux-gnu/rustc1.21.0

        2017-10-28 22:57:49  Keys path /home/john1/.local/share/io.parity.ethereum/keys/DevelopmentChain

        2017-10-28 22:57:49  DB path /home/john1/.local/share/io.parity.ethereum/chains/DevelopmentChain/db/125ccdc70e48df86

        2017-10-28 22:57:49  Path to dapps /home/john1/.local/share/io.parity.ethereum/dapps

        2017-10-28 22:57:49  State DB configuration: fast

        2017-10-28 22:57:49  Operating mode: active

        2017-10-28 22:57:50  Configured for DevelopmentChain using InstantSeal engine

        2017-10-28 22:57:50  Updated conversion rate to Ξ1 = US$294.65 (404030600 wei/gas)

        2017-10-28 22:57:53  Public node URL: enode://883300821...@192.168.0.104:30303

Be sure you see: Configured for DevelopmentChain.

5. Open http://127.0.0.1:8180 in your browser, skip the warning saying you are not connected to any node and follow the steps to create an account.

6. Go to Settings and check Contracts checkbox to see Contracts item in the main menu.

7. When you click on the item, Contracts view opens. Click Develop and you should see the web IDE where you can start writing your smart contract.