How do I get around black, square blocks?

You need to have an item that grants flight.

The list of items which grant permanent flight from the original game is:

• Lord Of The Pit
• Transcendence
• A Pony / White Pony
• Holy Grail
• Fate
• Spirit Of The Night
• Dead Dove
• Guppy or Lord of Flies (collecting 3 Guppy items or 3 "flies" items in one playthrough will give Isaac permanent flight)
• The Hanged Man (Tarot Card)

There are probably several more in Rebirth.

You can also clip through the blocks with two bombs.