They expect you pay to play in the Hearthstone Arena? I think not...
no. you get a daily every day which if you complete gives you gold. that daily can be reset by declining it in case you don't like it. you can accumulate up to three dailies... so what some people do is only log into hearthstone once every 3 days... complete the dailies and log out.
if you play casual or ranked, you get 10 gold per three wins, to a maximum of 100 gold (this doesn't include daily) each day. but this takes a lot of time which no one likes to do besides twitch streamers.
when you have 150 gold, do not spend it on a pack... because if you use your 150 gold for one single arena run, you get refunded back in gold, pack and dust and sometimes golden (foil) cards.
you only have to win 3-4 times in arena to be refunded an equal amount. 1 pack = 100 gold + 25 dust and 25 gold or 50 dust/gold = 150 gold worth
if you win more than 3-4 times... (maximum wins is 12) you get higher rewards, sometimes you can win up to 500 gold... always spend your gold on arenas, never on packs.
also you should play ranked up to level 20 every month so you get a new card back at the end of the month. for example today is the 5th... if you rank up to level 20... on june 1st you will receive a "ninja" card back.
also if you play rank and win 500 games using one single class... your hero portrait becomes animated and your hero power turns into gold.
if you truly want to brag, get a deck you like, make it all gold, make it so your class becomes gold.. and your enemy will be like "dayyyyyyyyyyuuuuuuuuuummmmmmmmmmm"
that's about it. also don't spend gold on goblins vs gnomes and black rock mountain... use real cash... the gold/cash ratio isn't worth it.