If a PC uses a cypher or an attack that causes a blindness area effect and succeeds the targets become blind for a certain amount of time. How do I tell how many rounds the blindness lasts and how the targets are inhibited? Do they just take a degree of difficulty in attacking? Two?
Duration depends on the descriptive text of the attack or cypher. Some will say X rounds, others will say Y minutes per cypher level, others might not specify one at all.
In Numenera, 1 minute = approximately 10 rounds of combat (see page 85 of the Numenera corebook), so units of time can be converted to rounds using that metric. For unspecified durations, typically this is left to GM fiat, though 1 round is usually appropriate.
Blindness in Numenera is treated as the affected character being in complete darkness (see the permanent damage table on page 114 of the Numenera corebook). When in complete darkness, but with the use of other senses they can use to determine where their opponents might be, a blinded target attacks at a penalty of 4 steps of difficulty in the defenders favour. Otherwise, attacks fail without a need for a roll, unless the GM wants to allow an expenditure of 1 XP for an affected player to get a lucky shot or uses an intrusion to make their NPC get lucky (see page 96 of the Numenera corebook).
Blindness is an Intellect damage type that means the characters acts as if in darkness until the effect ends.
Duration: Poking someone in the eye might leave them blind for a round, while a blinding flash might effect them for a minute or longer. A Detonation (Flash), for example, renders the target blind for one minute. Most device descriptions indicate the duration of effect.
Effect: If the blindness leaves the character with other senses to fall back on - like hearing the sounds made by an enemy - then they can attack modified by four steps in the defender's favour.
If the blindness leaves the character without other options - like they're facing spirits or stealthy ninja warriors - attacks fail automatically unless the player spends 1 XP to get a "lucky shot".
If the player characters blind an adversary, the adversary can get a "lucky shot" in with a GM intrusion.
Offsetting: A character Trained or Specialised in some way may offset some of the negative impact if not completely without sensory input. A character might also have an Asset that offsets blindness.
Source: I'm basing this on information from the Cypher System Rules. In practice, this applies to Numenera and The Strange also.