Here, I've summarized the most important items in dota for beginners. Learning these (over time) should be a huge help! Items after the arrow means the first item can be upgraded into these. I linked to the wiki pages so you can find more info about the listed items.
EVERYBODY WANTS THESE:
Healing Salve, Tango, Clarity Potion
Buy these items at the start of the game to regenerate health and mana lost in the lane. Salves heal you by a lot in a short time, but are one-time use and the effect stops if you take damage. Tangos have 4 charges that heal you a little, slowly, but the effect cannot be removed. Clarities regenerate mana slowly, and can be stopped like salves. As a general rule, buy one of each at the start of the game.
Boots of Speed (-> Power Treads, Phase Boots, Arcane Boots, Tranquil Boots, Boots of Travel)
Movespeed is very important on any hero, so all heroes get boots ASAP. From there, you can upgrade these boots into 5 different variations. Boots are too expensive to buy at the start unless you are confident you don't need the regen items. However, make them your first priority once the game has started. On carries, upgrade boots into treads or phase boots (never both!) as they give attack speed or attack damage. On supports, get arcanes or tranquils (again, only one) as they give mana or health regen. Late game, consider Boots of Travel for free teleportation (more on that below).
Town Portal Scroll
Allows you to teleport to any tower you own, one-time use and on a cooldown of 65 seconds. Use this to move around the map quickly and efficiently, escape from enemy heroes without stuns, or quickly help allies that are attacked. Rule 1 of dota: always carry a tp scroll.
Magic Stick (-> Magic Wand)
Every time an enemy casts a spell nearby, your magic stick gains one charge. When you use the stick, it depletes all charges and gives you 15 health and mana for every charge. It can be cheaply upgraded into a magic wand which has the same function, but also gives you some extra stats. The magic stick/wand is a very cost-effective item that is generally good on everybody.
CARRIES WANT THESE:
Damage items
This is super dependant on the hero you're playing. Just follow the in-game suggested items for these.
Black King Bar
Activating this item makes you magic immune for 10 seconds (-1 second for each use, minimum 5 seconds), meaning you can't be damaged or affected by most enemy spells. Extremely useful for staying alive and effective in a fight.
Blink Dagger
Allows you to instantly jump a large distance every 12 seconds. Essential for any hero that needs to close the gap with enemies quickly (some supports get this item as well).
SUPPORTS WANT THESE:
Animal Courier (-> Flying Courier)
The courier will deliver items to everyone on your team so they don't have to walk all the way back to base. From 3 minutes onward, it can be upgraded into a flying courier which is faster. You only need one courier per team.
Observer Wards
Everytime you buy wards, you get a set of two. Wards can be placed around the map to give a large amount of vision for 7 minutes, like a watchtower. Every 6 minutes, a set becomes available, to a maximum of 2 sets.
Mekansm
When you activate a mek, you and all allies around you are healed for 250 hp. Players can only be healed this way once every 25 seconds, so having more than one mek on a team is redundant.
Hope this helps!
( down 100 mmr today. Time to take a break by eating ice cream & playing MH4U.
