There are three main ways of filling the card slots: connecting hits, spending spirit, and having the opponent connect hits on you. In Hisoutensoku, each slot in your hand requires 500 card points to draw, unlike in SWR. There is no difference in how long the cards take to draw.
Connecting hits (blocked or unblocked) fills the gauges rather fast, with an amount that seems proportional to the attack's base damage. Firing B bullets gives you 30 points, firing charged B bullets gives you 50 points, firing any C bullets, charged or not, gives you 50 points. Doing a special gives 50 points, however there are some exceptions to this. Spells do not give points towards drawing cards. Taking damage also gives you points towards your next card, at the rate of 1 point every 20 health lost, meaning you gain a card from damage upon taking 10k damage. Chip damage and gradual damage, such as from Yuyuko's or Reisen's poison spells, do not give any card points, however.
Also, the Magic Potion card has its uses. The Magic Potion system card will greatly increase your spirit regeneration for a duration, and instantly recover crushed orbs. You know when you hear a "clank" sort of noise if you block incorrectly and see one of your spirit orbs turn orange? That means it's been crushed, which renders it unusable until it's restored. This would only otherwise be possible by waiting, so if you've had several orbs crushed by wrongblocking or Border Escaping, Magic Potions can be very useful. Or if you just like spamming bullets.