Speed running Diablo 2 is a different kind of experience than running the game normally. If you like to walk through the game at an average pace you should do that. There is no point in rushing through if your goal is to have fun with the leveling experience. However, some people like myself enjoy speed running through as fast as possible. Ladder resets become colossal time sinks as we rush to the endgame to farm gear to sell at a high price. Since demand is high and supply is low the prices are higher. The more people farming and getting gear the lower the prices will become. This means speed running the campaign to get to the endgame will give you a higher likelihood of being able to sell your items for a premium amount.
If you start as a class wearing a shield and you are wanting to speed run you should drop the shield now. Shield block frames generally take a long time. If you happen to block you will lose time and the monsters don't actually do much damage so blocking doesn't really matter. If you are playing hardcore you may wish to keep the shield. This is mostly a min/max thing, and not really a huge difference in my opinion.
Bloodmoore/Den of Evil
After starting the game you will exit out of town and follow the road to the Den of Evil/Cold plains. If you get to the cold plains first grab the WP and turn back. If you find the Den of Evil you should TP outside of it, and follow the path to the cold plains to get the WP. Take your TP back to the Den of Evil and continue on. It's important to note that when you kill monsters at this point in the game you should be picking up stamina pots, chipped gems, throwing items (Knives, javelins, poison pots, etc), staves, orbs, wands, amulets, and rings. You'll want to sell whatever is not useful for you so you can have gold to buy your ID and town portal books. On top of that, you should be buying stamina pots. Early game you will run out of energy and be forced to walk. This will slow you down a lot. Stamina pots will allow you to run through the acts without stopping.
It's important to try and think of the maps as a square. Looking at the images below notice how I added a compass in the top right. I use this for directions for example in the below picture the exit to Stony Fields is the northeast side of the map (the Northeast side of the square). Generally, the Burial Grounds will be in the corner of the map. Stony Field will normally be in the middle of the edge. Notice how Stony Field has distances on both sides of it that are almost equal. Burial Grounds doesn't it's mostly in the corner. I don't know if this is always true, but it does happen quite often.
If you're looking for a video guide of all these speed runnings tips watch the series by MrLlama found here. Lots of these tips are from his video guide and my own experience. You should use MrLlama as a source of info. He has fantastic videos explaining anything you'll need in Diablo 2.
Following the road will take you to the Underground Pass. Generally, you will want to find the waypoint and stones, but if you are trying to go straight through the game you may want to skip these. To find the stones they generally are just off of the road. If you are running on the road and have walls on both sides of you whichever side doesn't have a wall first you'll want to peak over that direction. The stones and WP may not be next to the road.
The quickest way through the Underground Passage is by sticking to the right. Generally, the exit to Dark wood is on the right side, and the exit to level 2 will be on the left. If you run into a group of the red Fallen enemies you can most likely turn back. Those are generally a dead end. You can kill them for drops/exp if you like, but it will slow you down.
Follow the road straight through the zone. If there are lots of mobs in a big group kill them for exp. You should be around levels 4-5 at this point. Remember to kill boss packs of monsters for big exp. If you are a completionist then you can get the scroll from the tree to rescue Cain, but it is not the fastest to do so.
Look for the waypoint and the tower. If you find the tower first then drop a town portal outside of it. Once you find the waypoint go back through your TP and clear the tower. Black Marsh's next level is almost always to the left, but it may be difficult to understand which way is left. It's best to use your starting location direction and then use that direction as "Straight". Use the image below to help you
Break the map into blocks. As you can see you enter in the "entrance block" The only way to move is to the southeast. This will be considered "straight" for this level. You continue in the only direction available. So you move to the "only block to move to". Then next area could be continuing in that direction, or the first possible left you can make. As you can see if you take that left into the block the only remaining path is the exit block which is also left. It may be easier to visualize yourself walking through this to get your directions. On rare occasions, it may be 3 rights to equal the left. Level 5 will have the Countess. She has a bug with her where she will not go through doors. Her minions will go through them whoever. If you follow the map below she will almost always spawn in the middle of the room. If you go the other side she will spawn in around 3 different spots. Tal Eth for Stealth body armor is a great use of runes. Stealth will give FCR, FHR, and FRW. For any fire characters, Tir Ral in a staff is great. It will give you +3 to fire skills.
Outer Cloister has 3 layouts available. If there is an open Square with the WP to the top right of the layout then you need to head to the left. If it has a cross with a WP in the top right then head to the top middle. If the WP is on the left you need to head to the right. Generally once in the barracks check the left then go straight to find the jails. If you find the smith grab the Malus and then leave. Once you get into Act 2 try to imbue boots for run walk. If you don't find the Malus don't look for it.
Jail 1 and 2
Refer back to the tower for how directions work in this area. For Jail Level 1 it will just be in the straight direction. It may not be dead straight, but the exit block is facing that direction. The waypoint will to the left. May not be dead left, but taking lefts should lead you there. This is not a hard rule. Jail 2 is generally straight as well.
The outer closer will be to the left. Remember to go back to Tower for more info on directions.
Avoid the tainted as they are a pain and will slow you down. The map never changes. Just go down to Catacombs.
Catacombs level 1
For level 1 it's just running around randomly and using your experience of playing the game to find dead ends and avoid running down them. Double doors with a hallway on each side are a good indication that there is an exit there.
Catacombs Level 2
The exit is always to the right of the WP. It also follows the same rules as Catacombs one with the two doors and the hallway being a good indicator of the exit.
Catacombs level 3
Blind run. Get lucky and use past experience of reading blocks.
Catacombs level 4
Level 4 never changes. Kill Andy. If you can lure mobs away from the big door to Andy, and then close the door on them, or just kill everything then Andy.
Hopefully, these tips and tricks are helpful for you. You can find a video guide at MrLamma's website. Speed running is a big part of ladder resets for me personally. I find it important to go hard at the beginning of the ladder to get my items early, but remember this isn't for everyone. You should honestly just play the game the way that is the most fun for you. If you end up in hell 3 months into the ladder but had fun that's a success in my book.