Written in blood
Bloodborne helps those who help themselves. While it'll go out of its way to give you as little information as it can get away with (it never even explains how to equip your sword and your gun), it will reward you for every little trick you learn in fine Souls series tradition. Even the tiniest revelations can make a huge difference, letting you bypass that brick wall you keep smashing into a little earlier than you would have otherwise.
Unfortunately, when you're starting an entirely new Bloodborne adventure, as you will in The Old Hunters DLC, those tiny revelations can feel like a river of hemoglobin away. But fret not, because when you're playing a game this tricky, there's no shame in learning from the suffering of others (here, or in the main game). Take my advice, and commit these to memory - carve it into a Caryll rune, if that helps.
Getting to the new area is easy, if convoluted
In a move that should shock no one, Bloodborne doesn't directly tell you how to reach its new DLC area, the Hunter's Nightmare. Thankfully, it isn't too difficult. After you beat Vicar Amelia in the Grand Cathedral (you'll know her when you see her), you'll get access to the Grand Cathedral lamp. Return to the Hunter's Dream, and the messengers will be waiting for you on the steps of the workshop with an 'Eye of a Blood-drunk Hunter'. That tucked into your inventory, head to the Cathedral Ward lamp and go out the leftmost door (the one that leads to Old Yarnham if you follow the path further). Under a tree to your right, there will be a dead body; stand next to it, and a giant purple orb will approach you. Let it touch you, and don't be afraid of what comes next - sit through the crushing pain, and you'll find yourself landing safely in the Hunter's Nightmare. 'Safely'.
You might not be ready to take on the new area right away
You may get access to the Hunter's Nightmare fairly early in the game, but don't assume you're ready to tackle it right then - I personally had to double the level I was at during the Vicar Amelia fight before I felt comfortable taking on the Nightmare. The stage at which you're ready to face the beasts within obviously depends on your skill - Souls aficionados may be able to merrily traipse through the bloodbath without difficulty, but don't feel bad if you're not there yet, because you're not supposed to be. Play through the rest of the game, level up a bit, and by the time you come back, those hunters won't seem nearly as formidable.
You might have to play the game over again
If you've already beaten Bloodborne at least once, you know that it immediately prompts you to start a New Game+ file that writes over your previous save. Unfortunately, if you went ahead with that new-game creation and then gave it a rest for a few months, you're in for a nasty surprise: you'll have to play all the way up to the Grand Cathedral to get access to the Nightmare again, and probably a lot further if you need those levels buffs to get by. That's a painful realization, and it may make you reconsider if you want to try out the DLC at all - that's your choice to make, but if you can stomach the extra few hours of play, the reward is well worth it.
There aren't many special tricks to beating the bosses
The Old Hunters' bosses are some of the most brutal you'll encounter in all of Bloodborne, not just because they're incredibly difficult, but also because there's no real special trick to beating them. Where many boss fights in the main game can be made easier by exploiting a certain weakness - the Blood-starved Beast will be distracted by pungent blood cocktails, and The One Reborn gets weaker if you kill the bell maidens surrounding it - The Old Hunters' bosses aren't so fragile, and you'll have to take them all on the hard way. So don't feel bad if you can't figure out the secret to taking them out - just keep at it, or better yet, get a little outside help.
Save your bloodstones
After you decide which weapon is your one true love and have it fully buffed, you might be tempted to spend your bloodstones on a less-enticing backup blade, or even sell them to get a few extra blood echoes. Don't do that to yourself. The new expansion holds a whole new armory of deadly gear, from a glowing moon-sword to a sloppy but beautiful sawblade-on-a-stick, so it's entirely possible you'll find a weapon that you truly adore in the Nightmare's darkest crevices. Having no bloodstones left to upgrade your new baby is heartbreaking, especially if you haven't leveled your Arcane stat enough to increase item drops significantly (side note: do that). So instead of trying to farm low-level enemies for low returns, keep a bushel of bloodstones tucked away for safekeeping. You won't lose anything but some throwaway weapons you didn't care about anyway.
Old Hunter partners can be helpful in battle, but aren't always up to the challenge
The Old Hunters introduces more than just a challenge map that'll ruin your self-esteem and new encounters that make Rom the Vacuous Spider look like a ladybug: it also distributes summon points near most of the major bosses, giving you the opportunity to summon NPC hunters to fight alongside you. However, it's worth remembering that they won't always be on par with you in combat, because their levels don't scale with yours. In fact, sometimes they'll be so far below your current level count that you're better off treating them like a distraction device than a true partner in monster-slaughter. Consider it on a case-by-case basis, and decide if it feels like summoning them (which costs one precious Insight each time) is really worth it to you.
You can use the chalice dungeons to get quick Insight
Let's say you do decide summoning those NPC partners is worth the cost, but end up calling for help so often that you run out of Insight. While progressing through the base game will usually help you get more (unexplored areas tend to have a lot of Insight-granting Madman's Knowledge, and you'll gain a few each time you encounter a boss), the Chalice Dungeons make for a quick pick-me-up when you don't have time to wait. A vast sequence of optional dungeons filled to the stalactites with beasts, it also has plenty of bosses that will grant you Insight when you first meet in battle, and even more when you make fillets out of them. If you want to make sure you have a nice stash of Insight waiting in case of emergency, don't even bother with the dungeons until you're really in need. That way you'll be strong enough to wipe the floor with early bosses, and won't have to break your back for a few extra sprigs of currency.
This really goes for all of Bloodborne, but bears repeating: you can do this. As difficult as the game is meant to be - especially The Old Hunters, which is effectively a set of challenge bosses when the main game isn't tough enough for you - it's not impossible, and once you figure out how to stay calm and in control of the battle, you will get there. Take your time and figure out how to take on each encounter individually, in the way that works best for you. This game is in the bag (the the weird monster-kidnapper bag) as long as you can keep your head.