General Tips

The Learning Curve in the game isn't that steep. Even if you didn't play Fallout 3 and New Vegas (the other two versions of Fallout are turn-based RPGs; the ones I mentioned have the same gameplay as Fallout 4), you can immediately learn the basics. However, it won't hurt following these tips.

Save often!

The game is kind enough to create multiple auto-saves but it will be better if you'll save often, usually before exploring deeper in a location, bartering, lockpicking, hacking, or trying something stupid. This will save you a lot of time, effort, and resources.

Almost Everything is Valuable and Usable

Supplies are scarce in the wasteland. Collecting loot, no matter how obscure they may seem will help you in the long run. Fallout 4 has a crafting system that will allow you to use the scraps you find into materials which in turn you can use to create various practical and decorative objects, and also serve as components for enhancing your weapons, armor, and Power Armor. You can collect as much loot as you can then store them in your personal containers in your first settlement in Sanctuary.

Man's Best Friend

Shortly after leaving the vault, you can find a trusty furry companion a few meters away from your hometown of Sanctuary. Follow the road leading to Red Rocket Truck Stop where you can find the lone dog. Talk to him to befriend him and he'll be your friend forever. Dogmeat (he'll get the name later as you progress in the first main story quest) is a very useful companion. You can ask him to fetch items for you, find containers with loot, scout for enemies, and carry a good portion of your items. Furthermore, you can also equip with dog-specific items such as light armors and collars. The best feature is that Dogmeat doesn't die. He'll be gravely wounded and will whimper but you can just use a stimpack to get him to action. Dogmeat is also a very effective combatant, capable of taking considerable damage, can rip of limbs, and pin down enemies to give you a clear shot. In short, after leaving the vault, find and befriend him and he'll be with you for life.

Assign your weapons and consumables

The game allows you to set up to 16 different consumables and weapons in each D-PAD direction. (4 each) By default, pressing the down D-PAD will select the Stimpak. This is the only fixed slot and you're free to assign whatever weapon you have in your inventory for easier and faster access. This will also save you the hassle of opening your inventory and selecting the weapons you want.

Health Management and Cooking

Killing wild creatures in the wasteland yield meat and other usable items. However, eating them raw will just give you radiation and an ample amount of health. This is solved by cooking these meats using a Cooking Station. Most settlements or cabins have these useful contraptions in their immediate areas. Cooked meat has no radiation and recover a lot more health. Most of the time, they're also "lighter" in weight compared to their raw counterparts, making them more ideal in both storage and health recovery.

Crops and Farming

In addition to crafting, you can "plant" various crops, fruits, and vegetables in your friendly settlements. These will grow quickly over time and you'll be able to harvest them regularly. Harvested crops can be "used" to plant additional copies of that plant, giving you a chance to build a steady resource to supply Food for your settlement, ingredients for your dishes, or simply as barter items you can trade with traders.

Avoid untreated Water

Unless you have the appropriate perk that will enable to become immune from the irradiated Water's negative effects, avoid staying in bodies of water for long since their radiation can literally melt you. Drinking untreated water also is not recommended since the radiation outweighs the health recovered. Don't worry about Dogmeat though. Your tough pal has no problems crossing irradiated water and even heavily radiated chemical leaks.