I had Mr. Super Cranky baby- the Tinkleberry.
First, take your kid to the doc. Make sure there is no ear infection or bladder infection. Especially if the kid pees a lot (like 15+ diapers a day). I wish I’d known to do this at a month- it would have saved us some agony.
Next I’d try the “magic hold” (colic hold). Lay kid face down on your forearm. Sometimes it works best with the head in the crook of your arm, sometimes with his head in your palm. YMMV. Hold like this (and maybe bounce gently) for at least 5 minutes. He may calm down quickly, it may take 5 min or so. If it works, DON’T CHANGE POSITION under penalty of death. I seriously think my kid spent his entire second month in this position.
Warm baths can sometimes help.
Stroller walks- might calm the baby down, and hey, you are sharing the joy of a new baby with others! 
Car rides (unless you have our kid, in which case the car is a hated beast).
Try feeding again- even if you think he only ate an hour ago. Sometimes fussy=thirsty.
Swaddling. They make a swaddler blanket thing with velcro for parents who can never get the wrap quite right (like us).
Mr. Pacifier- try a different brand/shape if one doesn’t work (ours only liked avent ones).
Colicky and fussy babies can literally drive you to insanity and depression. Switch the baby with another caregiver as often as possible and get away out of the house (even if only for 15 min) when it isn’t your turn. If stuck with an endlessly crying baby, remember when you are overwhelmed it is OK and GOOD to put the baby in his crib and take a 2-5 min break outside to get some air. Use earplugs- the crying can be painful and very very stressful. These aren’t to ignore the baby, just to lower the volume while you care for him.
One month is still the “crap! I’m NEVER gonna get off this damn couch!” stage. Trust me, you will. And trust me, not being able to accomplish more than showering/eating for the first 6 weeks is totally normal and not to something to feel guilty about.
Get sleep. Even if you have to have a relative or night nurse or friend watch the kid while you do. Nap good, all night better.
Our son was a mess until about 3 months. I promise it will get better- especially when the real smiles start.