When Kraken removed the XLM/EUR pair it became more difficult to buy Lumens without going through Bitcoin first. Not only is it hard to buy directly Lumens for fiat, but most exchanges require a long verification process and for someone that wants to grab quick Lumens with their Credit Card it can be a difficult, expensive and long process.
Soon other exchanges will be adding XLM pairs, but in the meantime you can use the Stellar DEX (decentralised exchange) to buy your Lumens. This has also the side-effect that you will become more familiar with the Stellar network. More trades directly on the network also will provide liquidity and allow for more efficient trades. Arbitrage traders can use the current low liquidity on Stellar in their advantage and earn more.
The beauty of the Stellar protocol is that it's open (like email for money). You get the same tools as big financial organisations doing their settlements. I think that we should encourage more users to directly use Stellar for their trades. Therefore, I will provide here a quick overview about the most important information you need to know when trading on Stellar.
Getting your fiat on the Stellar ledger
Maybe the most confusing part for newcomers is the connection between a distributed ledger and their bank account/credit card. To trade on the Stellar DEX you will need to turn your USD/EUR/CNY/etc into equivalent tokens on the Stellar network. It is important first to get familiar with the concept of anchors.
Anchors are financial institutions that hold your fiat/commodities/sheep/etc and issue an equivalent amount of tokens on the Stellar network. Because anchors hold onto your fiat it's important to find an anchor you trust. Depending on your country (note that some anchors operate in multiple countries) you can choose one from the list on Stellar's website.
Every anchor has a different way of depositing and withdrawing fiat. I really like Tempo. They offer Credit Card/Bank Transfer/Cash deposits and withdrawals and operate in more than 40 countries. Here are some instructions how to get your Tempo EURT tokens into your Stellar Wallet.
NOTE: You can buy the EURT tokens with USD, you don't need to use Euros.
Trading on Stellar
Now that you have your fiat tokens on Stellar you can send it around the world to anyone for an ultra low fee. It's like magic. Anyone who receives your token will need to use the same anchors to withdraw the fiat to their bank account or trade it for a token of a different anchor that is supported in their country. Mostly, users will want to trade it first for XLM (Stellar's native asset) before going to another token. That's also why XLM is called the bridge currency. If you have good TOKEN<>XLM liquidity you can easily trade for any other tokens on Stellar.
Trading is supported in many wallets, but there are also dedicated Stellar trading clients. My favourite is Stellarterm. If you look at the order book of XLM<>EURT you will see that the rate is really good for smaller amounts (up to $600). Even better than some big exchanges (Kraken) at the moment of writing this article. With more traders it will just keep getting better.
Getting your fiat to a Stellar anchor is usually much faster than getting approved by an existing exchange. It also has many other benefits: no trading fees, completely decentralised network, etc. I think that the Stellar DEX is just an amazing tool that is about to be discovered by the wider trading community. As you are part of the Stellar community you can be one of the first using it and having an advantage over other traders.