This guide is out of date, so don't take what i put to seriously. The base is still the same as what i use but my item choice is a little different.
I found that most players at the low-mid level aren't very good at counter harassing death prophet. So I only take 1 Tango just to cover the damage you might sustain. The Mantle of Intelligence is chosen in order to give a little extra damage and mana. The Sage's Mask is chosen in order to enable death prophet to almost spam the locust swarm spell. Once you get enough money quickly get a Null Talisman and then Phase Boots. These items will allow you to roam around and gank if you need to.
Death prophets locust swarm does very little damage for the mana cost until you get it to level 2 when you are at level 3. Be very careful when you use locust swarm, since it can cause your lane to push very fast and let your opponents get a few last hits under the tower. Every time you use locust swarm try to hit the enemy hero. Over time this will weaken the enemy hero enough to where they will have to go back to their base or allow you to get an easy gank.
There isn't really much of a reason for you to gank until level 6, since without Exorcism you can't dish out high damage very quickly. It is typically more effective to instead just push down the tower on your lane before you begin to roam, so that it will be harder for your opponent to notice.
The Eul's Scepter of Divinity is a great item to get on death prophet. The 30 movement speed on normal heroes doesn't do a lot, but with death prophet's passive. You are able to move at extreme speeds, especially if you have Phase Boots.
After the Euls normally comes Platemail followed by a Heart of Tarrasque. The platemail comes before the heart simply due to the cost of the Reaver. If the other team focuses you much then you will find it very difficult to get enough gold to get the Reaver.
After you get the heart, you should work towards finishing the Shiva's Guard. This item will give you the extra boost of intelligence that will make spamming locust swarm very easy.
Death Prophet has a good team fight ability with her Silence and Exorcism. She can also weaken the enemy team with locust swarm. If the game goes on to long you will find that you can't do any damage anymore with your spells. In this situation it becomes better to solo push a lane while the rest of your team fights.
If you find yourself beginning to push one lane while the rest of your team fights, then you will want to get a Shadow Blade. You can also get Boots of Travel if you want to.
Death prophet is generally a great pusher, since her locust swarm will destroy regular creep waves in under 5 seconds as well as Exorcism just murdering towers in about 10 seconds. I found that if I am left alone for 30 secs at level 16 I am able to destroy the tier 3 tower and both racks before Exorcism wears off.
The main reason to solo push is to hopefully pull a couple heroes off of their main group to allow your teammates to wipe the rest of their team. If they don't try to fight you, then you can just freely murder their base.
These items can be used freely to substitute for other items. Once you acquire the Eul's Scepter of Divinity then you can make a Shadow Blade any time after that depending on the situation. The Boots of Travel are also a good substitute for Phase Boots if you have some extra gold. death prophet is also a great carrier for the Gem of True Sight, since she is a fairly tanky hero who can escape very easily.
An alternate use for the Shadow Blade that not many people use it for is that if you activate Exorcism then the Shadow Blade then your army of spirits are free to murder randomly while you just watch safely while invisible. This can be used in order to get the other team to waste their powder on you and enable your stealth hero a chance to freely attack them, or just to deal heavy damage if they don't have any stealth detection items.
A lot of people don't like how I didn't include bloodstone and included shadow blade so i felt that I should justify it here rather than in the comments. I am a low-mid tier player so I don't know how this build scales to the high tier games.
I use the Shadow Blade in the rare circumstances. For instance if you are doing a split push while the rest of your team fights, then they will have to dedicate multiple heroes to stop you while the rest of your team pushes. If they try to destroy you then focus your team the shadow blade can be used to make a quick escape before they can use the dusts/stuns. The other advantage to a shadow blade is that if the other team has to have someone carrying dust then that will be 1 less slot for a different item that could hurt your team more. If your team has a stealth hero already then the shadow blade is pretty much worthless.
I chose the euls over the other items like the scythe, simply because it has a low cost and the ability to cast it on yourself. If the other team tries to rush you and you just need a couple seconds of invulnerability for the rest of your team to jump them then the euls works wonders. I rarely use the euls on my opponents. The only time it is really decent on opponents is to prevent 1 enemy hero from retreating for a little bit so your team can kill him. It is mainly just a self survival weapon with a movement speed boost to keep you moving around the other team throwing out your ultimate. It is also a cheep mana regeneration item that will allow you to invest in other durability items.
The Bloodstone is a good item. I just don't like to use it on Death Prophet. The reason is that dp needs mana regeneration in the early game and the bloodstone just costs to much gold. I found that in the late game I get enough mana regen from the euls to last almost indefinitely on the front lines. It is just more economical in my opinion to get euls and a Platemail than to get the bloodstone.