Note: there are far more than 1 team with some cross collaboration to make them compatible.

Can I try it now?

yes

Various clients, configured for testnet by default usually:

HTLC.me for Web (easiest and fastest to try)
Zap wallet
Eclair wallet for android
Lightning Labs testnet app

Try them with:

https://yalls.org/
https://starblocks.acinq.co/

More wallets:

lnd wallet
c-lightning wallet (part of elements project)
lit wallet

On Bitcoin's rootstock sidechain, lightning network is called "Lumino" still in early development and here is its white paper: PDF

Progress

Integration tests (between eclair, c-lightning, and lnd teams): https://cdecker.github.io/lightning-integration/index.html

Information

Learning resources about lightning network: http://dev.lightning.community/resources/

https://twitter.com/lightning
http://dev.lightning.community/
http://lightning.network/
http://lightning.engineering/

Videos

Stark, E. talks on importance of layer 2 (and layer 3).
Lightning network explained
Bitcoin's Lightning Network, Simply Explained!

Myth: I heard Satoshi hates layer 2

Satoshi invented state-channels, which LN takes to new levels

Hal Finney (who is likely Satoshi) also spoke of importance of layer 2.

Myth: I heard there will be centralized hubs

It's a rumor based on very early discussions about it that should not be the case due to significant flexibility. Can try observing the testnet lightning network clients above with very nice visual tools in some of them to show it's not the case.

Myth: I heard lightning can't scale

Simulating a Decentralized Lightning Network with 10 Million Users

Myth: I heard it would be too expensive opening and closing channels.

Yourself, possibly. Ideally there won't be a need for an average person to need layer 1 coins at all and all services, shops, and users typically stay on layer 2 "checking account" with some using layer 1 as "savings account". Settling might end up only happening due to dealing with a malicious actor with whom you would avoid dealing with in the future.

Multi-party channels can also make it significantly cheaper: source.

Decentralization is not easy and hence has some overheard cost. Privacy - more so. Main goal of decentralized cryptocurrencies is security, otherwise trusted centralized systems can always offer higher speeds and lower costs.

Myth? You can't go off-line

One directional channels with bridge nodes (if you don't get paid) can let you trade some security for convenience of being able to go off-line. The always online node can also be your own VPN like node that you might be able to rent or sold by someone as a service. Otherwise, not entirely myth as active channel users have to be online to update the channels. Sidechains would not have this constraint.

Who runs lightning nodes?

Anyone. Requires also running Bitcoin full node. Routing others payments would in turn provide income and incentive to run it. This should help both lightning node availability and Bitcoin full node availability.

Myth: I heard we can just increase block size forever?

Bandwidth is a limited resource and block size cap only exists as a security parameter, nobody wants to cap throughput for no reason. Any increases in bandwidth would cause price to pay for traffic to go up, pricing out users. Additionally, propagation times and network stability would decline as well. A backwards incompatible upgrade would cause node confusion of who is on which network resulting in lost or double spent transactions. Off-chain transactions such as lightning or sidechains aid. Tree-chains (sharding) would be another way to scale, but unproven theory at this point.

Detailed comment
Bitfury parameter study
Bandwidth analysis

Myth: I've heard we need smart contracts now so what's the point?

Good thing Bitcoin invented smart contracts, that's how Lightning Network is even possible, and they will only get better. Also, sidechains, like Rootstock, show ability to incorporate very different designs accessible for Bitcoin.

Is Lightning the only way for Bitcoin to scale?

No.

Sidechains with their own solutions are another way. Sidechains, in theory, can incorporate various protocols and have various risks and let each user decide what risk and what design to choose with each coin. DPoS that steem uses is an example of a protocol that would give a sidechain very high speeds.

Sidechain enabling Ethereum EVM for Bitcoin is Rootstock (explorer).

Drivechains are one of the ways to enable pegged Bitcoins movement across various sidechains, but there are other ways as well. Here's a list of interested sidechain projects.

Baseline lightning designs are not the only ones for layer 2 as well.

Sprites
Flow network
Group nodes
Flare Routing (PDF)
Duplex channels
Channel factories