Reddit reviews Trails of the Angeles: 100 Hikes in the San Gabriels

Some areas require permits, but not all do. Generally speaking:

National Parks:

• Are more likely to require permits.
  
• Are more likely to restrict camping to certain designated backcountry campsites only.
  
• Tend to have more restrictive regulations overall- National Parks tend to see higher levels of recreational use, and unfortunately, that means higher levels of abuse.
  
  National Forests:
  
  
• Are less likely to require permits (although some do require permits for certain heavily used, popular areas).
  
• Usually allow dispersed camping at sites of your own choosing in accordance with the Leave No Trace principles. There usually is also some minimum set back from trails and water that you are expected to abide by (this keeps groups from camping in the middle of a trail, and also helps to protect water quality from camping impacts). Camping may also be restricted in specific areas with certain sensitive ecosystems.
  
• Tend to have less restrictive regulations overall- National Forests tend to see (relatively) lower levels of recreational use.
  
  Usually, it's easier to pick an itinerary first, and then figure out if it will require permits. The best and most accurate source of information for whether a permit is needed would be to contact the management agency that oversees the area you intend to visit- the National Park Service if it is a National Park, and the US Forest Service if it is a National Forest. Another option is to pick up guidebooks for the area you intend to backpack in- these are usually written by experienced persons knowledgeable about the area, and a well written, up-to-date guidebook will contain information about regulations- including any necessary info about permits.
  
  Here is a guidebook for the southern Los Padres National Forest that looks decent: https://www.amazon.com/Hiking-Backpacking-Santa-Barbara-Ventura/dp/1643590138/
  
  Here is a guidebook for the Angeles National Forest: https://www.amazon.com/Trails-Angeles-100-Hikes-Gabriels/dp/0899977146/
  
  The National Geographic Trails Illustrated Maps also often include information about regulations (including permits). You can use the interactive map on their website to figure out which maps cover the areas you'll be hiking in most frequently, and then purchase those maps (if you look for the same map on Amazon, you can probably get it for a bit cheaper and also with Prime shipping).
  
  As you gain experience, you'll become more and more familiar with the regulations for the areas you hike and camp in most frequently- and the knowledge of what areas you need permits for will become ingrained.

The best place to check out local hiking books is your closest REI.

Here are a few of my favorites:

Moon Guides: Camping CA, Hiking CA
These are the most general as they cover the whole state.

Robert Stone: Day Hikes Around Los Angeles
This is just one of many hiking books he has in CA.

Schad Afoot and Afield: Los Angeles County

Schad: Afoot and Afield: Orange County

Harris: Afoot and Afield: Inland Empire

Shad/Turner: Afoot and Afield: San Diego County

Casey Schreiner: Day Hiking Los Angeles
Casey is the new kid on the block. He runs the Modern Hiker blog

Robinson/Christiansen: Trails of the Angeles

Robinson/Harris: San Bernardino Mountain Trails

Since you are in Arcadia you should visit the Theodore Payne Foundation. They are a
CA native plant nursery. They have a short hike on their property. They should be able to hook you up with some good hikes in the area, and a hiking club.