Pros

• Very bursty assassin
• Relatively mobile champion through his E
• Amazing game-changing ultimate
• A good team fighter
• Passive that hurts like a truck
• AOE crowd control with W

Cons

• Easily countered/kept low in lane
• Easily burst down (very squishy)

Sheen is a good item for Ekko's early-game. Sure, it may not do much with little AP, but could be easily exploited to win the early-game laning phase. You could catch an enemy off-guard with that damage, forcing him to recall early or set him up for a jungle gank. Building it into a relatively early Lich Bane allows you to fully complete your burst on an enemy, adding the damage your passive provides you could instantly burst down a squishy carry.

Luden's Tempest allows for a bit easier waveclear, especially with your Q and E helping you out. Plus, the additional 120 AP isn't so bad either.

Nashor's Tooth is also a good pick if you like sustained DPS and the extra Attack Speed and CDR bonus. Your 3-hit passive could be easily triggered if you have the needed extra attack speed, and you could abuse your skills through the extra CDR it gives.

Laning with Ekko is very similar on how you lane with other champs. If the matchup is toe-to-toe or clearly in your favor, never be afraid to turn the aggression on. Farm aggressively and poke your enemy laner when you get the chance. Deny him of any experience and farm, although make sure to ward your rivers so you don't get ganked in the middle of a fight. Never be afraid to ask for ganks. You need to be ahead of your opponent and make them follow your rhythm, not the other way around.

If you feel the matchup is NOT in your favor, get some jungle pressure in your lane. Or you could get fed off the sidelanes. Normally the bot lane would be a good gank path, since enemy carries tend to be squishy. Just watch out for the supports. When ganking, make sure you are aware where the enemy jungler is. If he's nowhere to be found, stay in your lane. If you gank without knowing where the enemy jungler is, the fight might instantly turn back around for you and lose even more experience. If your team's support could isolate the enemy carry for you, that'd be great, but an assist isn't so bad either.

Once you have your core items, harass your lane opponent to the point he has no choice but to recall or roam. Whenever your opponent isn't in his lane, use that chance to push, but make sure you're properly warded. With a Lich Bane, Ekko's split-pushing isn't that bad. Your E works on turrets. Although you should make sure that you are in a position to be able to immediately respond to unexpected team fights, or use that chance to gank the side lanes.

NOTE: The videos used below are mine, and I asked a friend to 1v1 me just so I could see how a Zed does against Ekko. I know the plays were pretty bad (especially my plays), they're just here to help give a visual reference to some plays.

Using Ekko's W

Play Video
Okay, so first off. Ekko's W, as you may know, gives you a shield whenever you're inside the zone, as well as stuns other enemies if they're in there with you, if not, it just slows them. In the above video, I miscalculated the W and Zed avoided the stun area, but since I was in the zone, I still got the shield and avoided most of the burst, resulting into a kill for me. Just shows making the best of a bad scenario pays off.

Using Ekko's R

Play Video
Keep in mind that Ekko's R makes him untargetable AND invulnerable. In the above video, Zed uses his ult on me as a last-resort in order to possibly burst me down. If you use your ult at the right time (usually a second or two after Zed ults you, I ulted immediately in this video, but it works so whatever), you could avoid the additional damage Zed puts on you. If you timed it right (not how I timed it), you could press it right before Zed's ult pops so you really receive no damage from his ult. In this scenario, I ulted immediately. Zed's ult still pops, but with less damage, as I didn't get any damage from his other skills.

First off, Ekko is an assassin. That means you should be targeting the enemy backline (the enemy AD Carry or AP Carry would be good choices). Let your AD Carry burst through the tank front-line (since that's what they're for anyway) and go once you see a free kill. Never go in alone or you will be eaten alive. Your ult is a perfect way to disengage in case a teamfight turns against your favor, although make sure your ult is in a perfect spot.

Your ult could be used either offensively or defensively. For example, imagine you're in mid and you're being chased down by the enemy team. Kite them towards your team, and just when your team is ready to respond, use the W + R combo. Make sure that once you use your ultimate, your W zone should be ready. Use your ult to get in the zone and stun all enemies and deal some damage (your ult does damage, follow up with your other abilities and proc your passive). Your team should be within reach and ready for cleanup. That's a teamfight that works in your favor.

Defensively, your ult could be used as an escape. If you ever find yourself in a fight you did not want, use your ult to escape to a distant location. Make sure you know where your ult is, positioning is key. No use escaping to an enemy tower.

Do not be afraid to abuse your skills, and don't worry about the mana costs. Early game Ekko's mana usage IS pretty high, but mid to late game you don't have to worry as much. Use your Q and E to proc your passive onto minions to easily get the last hit (your passive works on multiple targets at once, unlike Vayne's Silver Bolts.

Use your E to reposition yourself so that your Q can hit your desired target. Much like Sivir's boomerang, it follows you (unlike Gnar's boomerang which you have to catch to get the reset) so if you position yourself just right, opponents who think they've outsmarted your boomerang will still get hit.

If you're in a tight spot, you could use your E to dash over walls. It's basically a double-dash, so use your E to go over the wall for vision and strike a camp, or use your E to move to a spot where an auto attack would get you in range of a camp since your E teleports you to the target's location instantly.

Use your passive to your advantage. Do not be afraid to provide sustained DPS to a target. Once your passive procs on an enemy champion, you slow them, but you also get bonus movement speed. If you think you can secure the kill, kill it. You could easily escape using your ult.