Ideally, you don't, because critical fumbles are a terrible idea that draw out combat and make things even more swingy. If you're dead set on ruining your game with these cards, these are the things you need to keep in mind:
Use these changes:
- The cards speak about your 'base attack bonus' and 'confirming threats', but this is a thing that does not exist in 5e. My suggestion would be to simply roll a new normal attack after rolling a 1, if this is a miss, it's a critical fumble. This means your fighter is as likely to fail when they have to roll for a critical fumble as your wizard pretty much, but 5e did away with BAP being higher for fighters than for wizards. In 3.5, a Wizard using a crossbow would have had a far higher chance to fumble with it than a fighter using the same crossbow, in 3.5, the difference comes down entirely to their dex score.
- The cards talk about Weapon Focus and Greater Weapon Focus. These things no longer exist and there's no real replacement for them. You could homebrew something along the lines of 'having Great Weapon Master counts as having Great Weapon Focus' for every feat/class ability that involves weapons.
- There's a new weapon enchant in the deck. This is useless because the feat required does not exist, and 5e doesn't really do weapon enchanting. Most likely just ignore this one.
- There are two new fumble spells. I'd suggest not using them, or making them a concentration spell instead of their duration. They'll require rewriting to bring them in line with 5e spells, because 5e spells do not scale based on caster levels.
- Fatigued as a condition no longer exists. I'd suggest changing this to 'gains one level of exhaustion'.
- Sickened is no longer a condition. I'd suggest changing this to 'poisoned', which 5e generally uses for this kind of effect.
- Critical threats are not a thing, but making effects that cause you to target yourself and 'threaten critical' automatically crit would be insanely detrimental. I'd suggest simply ignoring mentions of 'threatening critical'.
- There are ability score drain effects in the deck, this is not really something D&D 5e tends to use. If you use these, you'll need to figure out what happens when you hit 0 in an ability, and how you recover these ability scores, as default 5e only has drain effects on monster abilities that specifically state how to recover from the effect and what happens if a score hits 0.
- Natural attacks have a lot of 'you cannot use this attack until healed'. This will result in wildshaped druids (and NPC monsters) essentially becoming useless until healed, because most creatures in 5e only have one type of natural attack.
- There are mentions of losing random prepared spells, but this is not a thing in 5e. I'd suggest changing this with "you lose spell slot, the level is determined randomly'.
- Flat-footed is not a thing in 5e. I'd suggest changing this to 'attacks have advantage against you for 1 round'.
- Weapons and armor taking damage or being destroyed is generally not a thing in 5e. There are some variant rules in the DM manual about it, but 5e mostly did away with effects that break your equipment, except for some monsters. Either remove the card, figure out some variant homebrew system, or just treat it as a 'disarm' effect or something.
- There are a lot of things that 'provoke an opportunity attack'. This will likely work fine in 5e, but is a lot less scary than it was in 3.5, because in 3.5 opportunity attacks were a free action. A mage casting a spell in melee combat would trigger an opportunity attack, if the fumble would then trigger one as well, you ate two opportunity attacks. In 5e, enemies will only ever get 1 reaction against you.
- Summon monster spell is no longer a thing. Homebrew it into something else, like summon woodland creatures or summon lesser demons.
- There's a card that says you can "only take a move action next round", but move actions aren't a thing in 5e. I'd rephrase this to "you can only move next round, you can't take any actions, bonus actions or reactions."
- The cards talk about 'enhancement bonus' effects, but these are no longer a thing in 5e. 5e mostly did away with effects that temporarily increase or decrease a statistic to speed up gameplay. I'd change it into, using strength as an example: "the target has advantage on ability scores, saving throws and attacks using strength".
- There's a card that says "the spell affects all targets within 30 feet of you". This was already a wonky effect back in 3.5, because what happens if it was, for example, a Detect Magic spell? Does everybody now detect magic? If it's a concentration spell, is it now a concentration spell for all those targets? I'd honestly just skip this card because it's way too confusing with spells that aren't damage/healing spells, and most likely will result in an instant TPK if this happens with a big damaging spell while you're close to your allies.
- There's a card that says "you are exhausted". I'd change this to "you suffer 3 levels of Exhaustion", which is roughly on par with what the old exhausted effect did.
- 'You made him bigger' has no real effect in 5e. In 3.5, scaling in size did all sorts of things for your armor class and damage, but it doesn't do this in 5e. I'd suggest changing this to "you cast enlarge on the target".
- There are mentions of the dazed status, this no longer exists in 5e. It is roughly the same as incapacitated is now, so use that instead.
- 'The target is hasted' is a bit hard to quantify because hasted is not a status in 5e, I'd suggest replacing this with "you cast the haste spell on the target".
- Caster's block would be crippling if this effect happens on a cantrip. If a Warlock gets this effect after casting Eldritch Blast, they're essentially dead weight for 24 hours.
- Caught your attack has a bunch of effect options that no longer exist. I'd suggest replacing it with "the target may use their reaction to grapple or push you".
- DR 5/- doesn't exist in 5e. I'd suggest simply changing this to "your target gains resistance to all damage for 1 round" (instead of 1d4 rounds). You could also go with "your target takes 5 less damage from all attacks for 1d4 rounds", but this isn't really an effect that D&D tends to do, the only one I can come up with is heavy armor mastery that reduces damage by 3.
- There is a reference to 'SR', which is spell resistance. This no longer exists in 5e. I'd suggest going with 'the target has advantage on saving throws against magical effects'.
- There's mention of needing to use 'full round actions', this isn't a thing in 5e. I'd suggest replacing this to 'you gain no benefit from Extra Attack, and you can't use bonus actions to make extra attacks'.
- Power transfer assumes that there are generally powerful magical effects on the caster, but this isn't really the case in 5e, where most powerful magical effects require concentration. Expect this card to never do anything. The same goes for magical vaccuum, unlikely to ever dispel more than maybe a Mage Armor.
- Confused isn't a thing in 5e. I'd suggest simply going with 'blinded' instead of trying to come up with random attacks, it fits the theme fairly well and takes less time. If you don't mind taking extra time, treat it as the 'Confusion' spell being cast.
- 'The target may give you one suggestion' is weirdly worded. You can give people suggestions all the time, that's not an effect. I'd add "as if they had cast the suggestion spell on you".
- There's a card that doubles armor and natural armor bonuses. This isn't a thing in 5e, and I'd highly recommend against trying to homebrew this because of bounded accuracy. Instead, give attacks against that target disadvantage.
- Nauseated is not a status in 5e, use 'poisoned' instead.
- Range increments are not a thing in 5e and this one is hard to homebrew. Perhaps something along the lines of "your weapons short range is halved", so you get disadvantage at a closer range.
- 'A stinking cloud appears' is a reference to the 3.5 spell. Luckily enough, it also exists in almost identical form in 5e, so simply treat this as if somebody had cast stinking cloud.
- Mirror images are a reference to the mirror image spell. I'd suggest simply reading this as "you cast the mirror image spell on your target".
- The Rod of Wonder table has been changed, but if you're going with random nonsense anyway, might as well roll on the new Rod of Wonder table, but perhaps a safer choice is to roll twice on the Wild Magic Table from the Wild Magic Sorcerer.
- 'You threaten no squares' is 3.5 language for "you can't take opportunity attacks".
- Shaken is not a status in 5e, simply use 'frightened' instead.
With all these changes, you should be able to use the deck without being completely confused as to what the cards expect you to do. I'd still recommend entirely against it because it'll slow down the game, will result in random TPKs because your Wizard suddenly cast Hold Person on everybody in your party and has a potential of randomly shutting down characters for 24 hours, but you do you.