Most of times, the first meeting with logs for many players takes place when they feel a need to improve so in this part of the guide I'll focus on checking personal performance and comparison between 2 players.
First of all, we have a summary tab for a specific player that shows you literally everything player related for any given fight: stats, gear, talents, artifact traits, damage/healing done and taken, etc.
So if you want to compare yourself to another player, you can easily see now whether there is a disparity not only in spell/resources usage but in more 'general' matters like for example different talents for a specific fight, different Artifact path taken or Legendaries equipped.
There are 3 options of comparison in WCL:
1. Compare reports.
Compares one full raid report (all fights) to another. To use this option you should copy the numbers and letters chain after the word 'reports/' into the 'Compare with URL' line.

2. Compare players.
Here you compare 2 players in the same report/fight. Very useful when you have 2-3 players of the same spec that are not performing equally. 

3. Search for similar to your parses.
A great option that actually shows you how other players of your ilvl were performing in the same fight (difficulty, fight length, amount of raiders). You can even check whether these players were using the same talents, legendaries, trinkets, etc.
This option is much-much better than just picking from random parses or, even worse, comparing to the top-10. Please, do not compare yourself to these parses if you are not around 90%+ by yourself looking for specific tricks and clearly understanding how the top was achieved.

Do not forget to choose the right filter in 'Select Metric'.
 
What can we check before comparing ourselves to other players:
- dps/healing affecting self buffs uptime:
Many classes have to maintain certain buffs uptime close to 100% in order to dps/heal efficiently.
You can check it in Buffs > Self-Applied tab. Here you can see not only abilities but potting and pre-potting, trinkets and enchants procs and thus be able to compare their efficiency.
For example on this screenshot we can see an enhancement shaman with a very good Legendary. They maintained all the dps self-buffs close to perfect, had a trinket with a great 40% proc (or just being lucky in this fight) and double-potted:

 
While this enh shaman had a very poor dps buffs management and didn't use dps potions at all:

 
- amount of dps/healing CDs used can be checked in Casts tab:
This is easy enough - take your fight length in seconds and divide it on the amount of ability casts. If you were doing it right, the amount of major CDs (2-3 min) used should be max possible (if not assigned by a RL to hold on for the timed bursts) for the given time, the amount of regular CDs (30-60 sec.) shouldn't be less than (max-2).
The amount of major CDs used is slightly less for the healers because we are not blowing healing CDs right on the start.
Note that in most of the fights you wouldn't be able to achieve 100% amount of possible CD casts because of movement or executing certain mechanics but you still should aim for this.
Let's look at an example in Nythendra Mythic kill log of some resto shaman that were worried about their healing numbers. Fight length 8:13 (493 sec):

Healing Tide Totem (3 min CD): 2 casts of 3 possible in a 8 min. fight
Spirit Link Totem (3 min CD): 0 casts of 3 possible
Gift of the Naaru (3 min CD): 1 casts of 3 possible
Gift of the Queen (45 sec. CD): 5 casts of 10 possible
Cloudburst Totem (30 sec. CD): 10 casts of 16 possible
Healing Stream Totem (30 sec. CD): 8 casts of 16 possible
As you can see, they hardly maintain 50% of CD casts and this is the main reason of their low healing numbers.
 
- amount of regular casts:
Some players just cast slow. They don't make mistakes in rotation but rather have some kind of a delay between casts while thinking about their next step or trying to change their positioning too frequently.
If you can't find any significant problem in applied buffs, gear, consumables or the amount of CDs used, try to check the total amount of casts and compare it to other players of your spec during a similar fight.
For example here you can see 2 Demon Hunters with the similar gear and talents in a similar fight but the difference in their amount of casts was about 25% that led to ~30% difference in Total Damage Done (143M vs 233M):

The actual damage / healing  comparison is done in 'Damage Done' tab for dps players

and 'Healing' tab for healers:

 
- focused targets:
We all know that sometimes high parses are achieved by dpsing wrong targets like AoEing adds instead of focusing or staying full time on the boss instead of following priorities.
You can check whether a player was playing 'right' in 'Damage Done' tab, choosing 'Done to Enemy' from the dropdown menu. Hovering your mouse above the enemy name will show who dps'ed it. 
In the same tab you can choose 'Done by Source' from the dropdown menu. In this case, hovering above every player's name (or clicking it) you'd be able to see how they split their dps between targets.

 
- Resources tab:
Very useful for the healers to check their mana management during fights (choose 'Mana' from the dropdown menu). Shows mana spent and mana gained from different sources like trinkets and potions.

 
- Deaths tab:
Note that some people look only at the killing blow and thus sometimes assume wrong the cause of death.
You should always click on the questioned player name and check the last 30 sec before the death: whether they used personal damage mitigation abilities, healing potions, did they received enough direct healing, etc.
 
- Replay:
You can see a modeled video of the fight and check every single second of it for every player.

 
I tried to cover mostly the basic features of WCL in this guide, there are still much more.
If you have any questions, don't hesitate to ask :)

Hi,
So I have recently returned to raiding, and am playing a disc priest for the first time. This is the first time I have raided as a healer, but have tanked and dpsd in quite high end guilds in the past. I am rather competitive, and another disc out healing me tonight has prompted me to make this post.
I don't feel I am doing anything hugely incorrect, but any tips you can give would be very much appreciated.
The logs I am linking is our normal mode clean up raid, and being so, we had our tank healing in terrible gear at some points, had 2 warriors tanking at others and 2 discs healing the whole way through, not to mention boosting a social from the guild. Needless to say, not a great raid set up. As well as this, I don't actually feel preformed to my usual standard, but that's probably an excuse I am making because I got out healed >.>
Anyway, without further ado, here are the logs:
http://www.warcraftlogs.com/reports/3PMfDwVaTZgzXvN8#type=summary&source=52
Here is my armoury:
http://eu.battle.net/wow/en/character/outland/Tetonic/advanced
And here is the other disc:
http://eu.battle.net/wow/en/character/outland/Nailin/advanced
Thanks in advance for any help you can give me.
Tetonic