Going into this process, I thought, "Yeh, I'm kind of clued up enough, and some how fudged my way thru Tezos, this should be a breeze!"
Well, I have to tell you, if you come in wet behind the ears, be prepared for a whole lot of learning! Tezos was a walk in the park compared to this!
But first, I'll explain the best I can, how the token sale works with EOS, as it's a little different to others. Their market cap of EOS tokens, is limited to 1 billion.
However, unlike other ICO's, EOS opted for a slow release, over just under 12 months. 200,000,000 were released during the initial opening of the ICO, and sold over a 5 day period. 700,000,000 are being released in 24 hour blocks, at a rate of 2 million per day for 350 days, and the remaining 100m will be preserved for block.one network.
What I really like about this approach, is unlike many ICOs where there's a dumping of all coins in the market, this slow-release method allows the market to set it's price daily in each 24 hour block, so in effect, by the time the full release has occured, it's averaged out over a 12 month period. How many EOS will you get? Well that's the lottery! As there is only a total of 2 million daily, and whatever amount is pledged in total in that block, shares their proportionate amount of EOS.
For example, if you were the only person to contribute 1 ETH to that 24-hour block, then you get all 2 million. If 100,000 ETH is donated, then for every ETH pledged, they get 20 EOS. And because each 24 hour block is published live with number of tokens released, it's transparent costing, so the market can adapt daily.
Coins are already able to be purchased on a few exchanges today (such as coinspot) and they represent approximately the average of current investments released. However, there's a reason I decided to buy my tokens direct, and that's because the exchanges selling them, haven't done a good enough job of convincing me they'll hand over my private keys upon final fulfilment of the ICO.
There are 2 ways to fund this ICO, both require ETH. I will explain the method I chose - using the metamask wallet. For me, this seemed the most straight forward. The other option is using MyEtherWaller (MEW), however there's additional steps to getting your EOS tokens back after completion. 
You'll need to download the metamask wallet, which can be found here: https://metamask.io/
They do a good job explaining how to set this up with this video
Now you'll need to fund you wallet. This step is pretty straight forward, you just need to access your public key from metamask. Do this by clicking on the metamask icon on your browser, selecting your wallet address.
Because the token sale is funded by Ethereum, go ahead now, and transfer your chosen amount of ether to your new metamask address. Once the transaction is verified, you'll see if appear instantly in your wallet.
Now you're ready to get started!
These next steps are only for funding via the metamask wallet.
Now go to the EOS website (eos.io). You'll be given 3 main options, you can elect to signup to their newsletter (I registered 2 weeks ago and haven't heard anything, but why not!). But we're only interested in the token option for now.
Go ahead by clicking TOKENS, this will take you to the current token distribution period. You'll see how long left in this period before it expires, and what level of investment is held already. Now go ahead and select "GET EOS"
This will bring you to the token purchase agreement. You want to read, tick all 4 boxes and confirm by clicking continue. FInally you'll be brought to the instructions page.
About 2-3 pages down, you'll see the sub heading "How to participate". Read through this paragraph carefully. EOS tokens are allocated at the end of your nominated period. By default, most people will contribute to the most recent time period (24 hour block), however you can choose whichever one you want. Just know that if you nominate in the future, you will need that block to complete fully before you can claim your tokens
You will need to next make a transfer of whatever amount of ETH you wish to contribute, to the EOS token sale wallet address. The address is 0xd0a6E6C54DbC68Db5db3A091B171A77407Ff7ccf- but always check the site and don't trust this. To be 100% sure, you can visit this address on etherscan.io and can get some comfort knowing that millions of dollars already have been pledged to this token address,
But before making this payment, you'll need to go back into metamask, and add another network by clicking in the top left of metamask (to the right of the little fox) and select custom RPC. You then need to add the following https://rpc.eos.io into the field, and save. More instructions are available here via the eos site
Now - the steps the site tells you to follow, is to join this new RPC before going to the distribution app (next step). I found this didn't work for me, and it worked fine being connected to Ethereum Main Net. When you follow this next step, if you don't get past the initial screen, then try the EOS recommendation, and connect to this network from your metamask plugin. When it's done it's thing (this can take some time), you're ready for the business part of the transaction.
Now, head over to the Distribution App - this is where the portal via your custom RPC will listen for your deposit via the metamask transaction. Note - this site is slow to load, and especially when it's nearing a 24 hour block, it tends to be congested - so be patient, and you may have to reload once or twice if nothing happens. You'll be greeted with, "EOS Token Distribution - The Interface is loading, please wait..." while this is happening.
FInally you'll load up the payment page. You now want to select one of the 4 boxes listed in the top right - GET EOS TOKENS. You'll now be given some choices as to which period you wish to contribute to. Remember as I said above, if you select a future date, the final step below Claiming your tokens cannot be done until that 24 hour block expires. ie. If you choose December 25, you will not be able to go back and claim your tokens until December 26.
Once you've selected your period (let's assume you nominate the current block), you'll be asked as to how much ETH you wish to pay. So go ahead and choose your nominate amount, and click SEND ETH. This action will pop up with a metamask confirmation box. Assuming you have enough in your wallet, it's simply a matter of confirming this action, and bang - your ethers are on their way!
Now while you're waiting for this to be validated on the blockchain, you should also go ahead, cruise back to the top of this page, and select generate EOS key. These are your public & private EOS token keys. Back these up somewhere very safe, like the password manager in trezor.io cold-storage - you may not do anything with these tokens when you get them for up to 12 months, so you want them kept secure. Remember: This post is purely for this reason, as purchasing EOS on an exchange means you won't receive your keys until possibly June 2018, do you want to risk them with your private keys for that amount of time?
By now, you should see your transaction match up on the current period, it will show on the right side of the ledger along with your ETH payment amount.
Assuming your got this far, without issue - take a breath, sit back, and wait for your block to complete. Well done, the hard work is over!
Assuming you did all the above without issue, you'll see a previously greyed out option, "CLAIM EOS TOKENS". This process will now send your allocation of EOS to your metamask wallet. You'll see towards the top left, your amount of EOS will be shown as "unclaimed EOS tokens".
So go ahead and start this process by clicking this button. Once again, metamask will do it's thing, and pop up confirming transfer of tokens.
NOTE: transfer of the tokens requires miners to match up the transactions on the blockchain. For this, there is a fee. I'm not sure exactly, however I estimate it to be approx $2-3USD per ETH contributed. When you try to transfer, you'll either have sufficient or not. It will tell you how much is needed to send your tokens over, so you may have to "REJECT" this transaction, and once again, send more ETH to your wallet to cover this (as I had to).
So go ahead once again and start the transaction. Assuming you have enough in your wallet this time, your tokens will start the process of coming over to your metamask wallet.
You can follow the transaction via the link to etherscan on metamask. When the process is complete, you'll be able to see your shiny new tokens in the TOKEN tab of metamask.
And that my friends is it! The simple, quick & easy process of acquiring EOS tokens via their ICO site.
I hope you were able to follow, I'm certainly no guru in ICO's nor claim to be, but sometimes it's easier to follow a noob who bumbled their way through it successfully.
I'm only a young minnow in this awesome community trying to find my way, so if you find any value in my post, please help me out by following, resteeming & upvoting. I'll do the same, as I love to follow and support people who support me.
Thanks guys. I look forward to sharing some EOS with you all!
@imrob