Attack Pattern: There are two kinds: regular ones and Pile-Drivers.
The regular ones fall from certain Para-goombas in groups of about four. They float back and forth and fall off the bottom of the screen unless they latch on to Mario. Once they grab Mario, they will stay on him until shaken off.
Pile-Driver Micro-Goombas hide under blocks and try to crush anyone who gets too close by jumping on them. They will lift the block a couple of time before jumping, so watch out for them!
Basic Fighting Strategies: The regular ones can't be killed, either avoid them or jump rapidly to shake them off. The Pile-Driving kind can be beaten with any attack except fireballs.
Advanced Strategies: If you see a Paragoomba dropping Micro-Goombas, wait for it to land and then jump over it. You can often run under them just after they lift off so that no Micro-Goombas land on you.
As for the Pile-Driving ones, Jump attacks work best. Just stomp on a brick when you see the Micro-Goomba lifting it. They can jump about five bricks across and three or four bricks up.

Attack Pattern: The only time you will run into these creatures in Super Mario RPG is while fighting Hidon in the Sunken Ship. Hidon tosses them out four at a time, and they use surprisingly powerful regular attacks.
Basic Fighting Strategies: Thunder, Poison Gas, Geno Beam, and Fire all work quite well, but regular attacks may be your best bet. It takes two or three timed-hits to beat them. You shouldn't waste too much energy on these guys anyway, Hidon is the real threat.
Advanced Strategies: Have characters whose magic attacks don't work well on Hidon fight these guys instead. If you have Mallow in your party, you can wipe them out with a couple of Thunderbolt attacks. Also note that Hidon won't spit out any new Goombettes unless you defeat all four of them, so you might want to leave on on the battlefield until Hidon is defeated.
Blocking Goombettes is very important, because it reduces the damage they cause a lot! Goombettes will walk up to one of your party members and bite three times quickly: press A as they bite for the third time to block the attack.

Attack Pattern: They attack much like regular Goombas, wandering around until they see Mario, and then charging at him. They are very small, so you may not see them until they hit you.
Basic Fighting Strategies: These guys are chumps! They can't cause any damage to Mario, and if they try they will die. Needless to say, any attack works.
Advanced Strategies: Use a Ground Pound (a.k.a. Butt Stomp) to kill them and get a coin. A regular stomp or a low kick will work as well.