For Video LPs:
Cut the grind and repeated sections. Just cut them. To understand why, watch any new-ish LP of "I Wanna Be The Guy" (they're all terrible).
If you get stuck, be entertaining about it (getting mad, being baffled, etc)... for about three minutes. Longer than that is excruciatingly annoying unless you're the king of hilarious tirades.
Use good editing software. Experiment with the free ones for a couple hours to find which one you like.
Don't use a camcorder pointed at the screen. Use a capture card for consoles and a direct-capture tool like FRAPS or BandiCam for PC.
Blind video LPs are good for horror games and arcadey games only. If you're going to play an adventure game or game involving notable levels of dexterity and skill, do us a favor and play the whole damn thing first.
Talk. Not only will this help you dodge sound-triggered copyright bullets, but it's infinitely more interesting than just straight gameplay footage. If you're really averse to talking, use unintrusive caption commentary.
Know when to shut up. When major plot points are going down, no one cares about your commentary anymore. Use your talking wisely.
If you have to be funny, be so sporadically. Funny voices and ad-libbing extra dialogue are absolute no-nos unless you're a really, REALLY damn good voice actor (like, Mel Blanc tier).
Try to stay three videos in advance (four if your video segments are less than ten minutes), unless you're going for audience participation.
You are your own worst critic (unless you're DarkSydePhil). If you turn a critical eye on your work and think it's watchable, then people will watch it.
For Screenshot LPs:
Edit, edit, edit. Edit even more than you would a video LP. When I wrote a (tragically forever unfinished) Daggerfall LP, I would occasionally throw out my whole rough draft and start from scratch.
Make all your screenshots fun to look at. Just because the level is brimming with steel walls doesn't mean we need to see every last one of those walls (unless you're doing a very well-executed joke about the prevalence of said walls). Nor do we need screenshots of all 80 encounters you have with standard brown imps in the level. What's more fun to look at: Lara Croft rebounding up improbable ruins hanging out of a cliff over a gorgeous lake, or Lara Croft flipping over a tiger over and over?
Combat is secondary in a screenshot LP. Focus on the stuff that's fun to talk about and is varied. "And then I shot him in the face" loses its punch 500 instances in.
Add more of a personal touch than in video LPs. Your writing style should be instantly recognizable and engaging, otherwise people won't engage.
General LP tips:
Pick a good game. Street Fighter IV is not a good game to LP, because it's extremely short, the story is nonsensical and ultimately unimportant, there's a limited moveset, and all of its appeal lies in the skill required to play it. Better choices are adventure games, randomly generated games like Minecraft, and RPGs. (Obviously, there are exceptions, but it's up to you to decide what's an exception and what's not.)
Pick a game you LIKE. I can't stress this enough. If you pick a game you don't like, you won't finish the LP unless you're being paid, guaranteed.
Don't expect it to be an overnight success. My LP attempts picked up steam very slowly, but after a couple weeks, hit their stride and really got going. You may even not get any replies to the first couple of posts. Don't be discouraged, persevere and people will come in and read it.
Post LPs on SomethingAwful's Let's Play board for best coverage. Warning: They're picky. The Escapist is good for garnering a small but dedicated audience.
Commit. My LPs died early deaths because real life dragged me away and I never returned to them. It's disappointing and demoralizing to have dead LPs that had an audience. Set your sights on it and go, don't stop.