If a creature with wither or infect deals damage to a creature, the controller of the creature with wither or infect puts that many -1/-1 counters on the second creature.

Obelisk Spider's first triggered ability puts only one -1/-1 counter on the creature, no matter how much combat damage it dealt.

If Obelisk Spider deals combat damage to a creature but that creature isn't on the battlefield as Obelisk Spider's first triggered ability resolves, most likely because Obelisk Spider killed that creature already, that ability won't put a -1/-1 counter on it.

Because damage remains marked on a creature until it's removed as the turn ends, the counter Obelisk Spider's first triggered ability puts on a creature may cause previously marked damage to become lethal.

If Obelisk Spider deals combat damage to a creature at the same time Obelisk Spider is dealt lethal damage, its first triggered ability will put a -1/-1 counter on the other creature. However, because Obelisk Spider has left the battlefield before that ability resolves, its last ability won't trigger.

If you put one or more -1/-1 counter on each of multiple creatures at the same time, Obelisk Spider's last ability triggers once for each of those creatures.

In a Two-Headed Giant game, Obelisk Spider's last ability causes the opposing team to lose 2 life and you gain 1 life.