Balatro gameplay has no definitive stages, instead each run has multiple rounds of boss blinds that have to be defeated by achieving a certain score through playing various poker hands.
*Information below is based on the latest version of Balatro (0.9.0q-DEMO) unless otherwise stated.
Pre-run[]
Upon clicking the play button, an interface will emerge with three tabs at the top (New Run, Continue and Daily Run).

The Continue tab displaying various information about the unfinished game

The New Run tab displaying different stake and deck options and the custom seed

A game file displaying potential stake difficulties; the base difficulty White Stake is seen at the top left
The interface defaults to Continue if there is a previous unfinished run, and displays the stake difficulty, deck type and various other information about that run. The player continues from where they previously left off if they click on "play".
If there are no previously unfinished runs, or if the player wishes to start an entirely new run, the interface switches to New Run instead, where different stake difficulty (only White Stake difficulty so far) and starting deck (3 out of 15 are available in the demo) options are available. There is also the option to play a seeded run where the player can input a custom seed. The seed pre-determines all the boss blinds and shop options available in that run but disables discovering new items from the collection and score statistics are disregarded (joker, and consumable stats still track your seeded games). Versions prior to the demo unlocked higher difficulty New Game + options upon a successful run that defeated the final boss blind, with each higher difficulty setting adding more "+" signs and faster ante scaling.
A tutorial run is loaded if the player has never played the game before, where Jimbo, the game's mascot joker, will explain the various interfaces of the game while leading the player through an example run [please verify].
The Daily Run tab is a recent addition of the demo version, but no playable interface has been implemented so far. When clicked, it displays a description of potential features of the new game mode, promising daily challenge runs with unsellable Eternal Jokers, custom starting decks, unique rulesets and a competitive ranking system.
Actual Run[]
Once the player begins a run, they are presented with the first set of three blinds: the Small Blind, the Big Blind, and the Boss Blind. The first two of these can be skipped to receive Tags that provide a boost, but the Boss Blind must be defeated to move on to the next Ante.
To defeat a blind, the player must select cards from their hand to play poker hands and score chips. A given number of discards are available to assist with creating better hands. If the player is unable to reach the blind's chip requirement in the allotted number of hands, the run is lost, and the player must restart from Ante 1.
Upon reaching the chip requirement, the round ends and the player receives money: a set amount depending on the type of blind defeated, plus $1 extra for each remaining hand, plus $1 interest for every $5 the player already has. This money can be used in the Shop to buy Jokers and Consumables to improve the run.
When Ante 8 is completed, the player wins the run, and is allowed to either start a new one or continue in Endless Mode, letting the player keep going for as long as they can before the blinds become too difficult to defeat.