If your inventory is full and you can't fast-travel, take Buffout — it'll increase your strength long enough to finish your sweep through whatever location you're in, and allow you to fast travel back to your base. No Buffout? Drink alcohol, which will also give you a strength boost, albeit a lower one.
... but only if you take them off a weapon before you scrap it. You can also take mods off weapons you find and put them on weapons you already own — including "legendary" gear you find on legendary bosses.
If you get into trouble, or see an enemy you don't think you can kill, use Fallout 4's new sprint function to get the hell out of there. And don't be cute and use VATS to try to kill it with a critical hit — VATS and sprint use the same meter. Also, don't worry about your companion if they keep starting fights. Eventually they'll get away and come back to you.
There are perks for different kinds of weapons that give them better damage and effectiveness, so it doesn't hurt to pick one based around the best weapon you find early. The 10 mm pistol is useful for a long time, so points in pistols early can't hurt. (Don't run in Power Armor)
Fallout 4 communicates in a lot of ways, but its clearest voice is always death. Death can mean a lot of things in Fallout 4, but if you die and lose more than a few minutes worth of progress, what the game is telling you is to save more often. You can increase the frequency of your autosave in the options menu, which is great, but remember that this setting only applies when you go in and out of your Pip-Boy. But good news! Quicksaving is available in the pause menu and is incredibly fast. Also, maintain a lot of save files. Our friend Chris Plante wrote about the great time he was having in Fallout 4 until he found himself stuck in an elevator after multiple in-game glitches. This is awful, and ideally it won't happen. If it does, the best way to fix it shy of a massive social media campaign is to save often, and maintain staggered saves. This means you should select "create new save" in the save screen. This could be the difference between losing 20 minutes or losing everything.
When you craft new weapon mods, the parts you replace go into your inventory. This adds up over time! You may be able to dump 50 pounds of weight if you store your mods in the workbench instead.