How to get to Lugansk and Donetsk. Apply for a pass to go through checkpoints. Crossing border with Russia
As for 2017 there are no restrictions to travel in or out of Lugansk or Donetsk city or other towns controlled by so-called Lugansk People's Republic and Donetsk People's Republic. There are two ways to get inside the territory which is not controlled by Ukrainian authorities. One way is to go via checkpoints in Lugansk or Donetsk Regions. And another way is to go through Russia-Ukraine border where it is controlled by pro-Russian militants. If you go via checkpoints you will need a pass issued by Security Service of Ukraine. The pass is free, you just need to apply online and usually it's ready withing 10 days. Every day there are about 20 000 people crossing the contact line via those checkpoints. There is only 1 operating checkpoint in Lugansk Region and there are 4 checkpoints in Donetsk Region. Some people also travel via Russian border, in that case no pass is needed, people can go with their local Ukrainian passport and they don't need international passport to go to Russia. For example a bus from Lugansk to Kharkiv costs about 25 USD one way and the price is almost the same if you go via checkpoint or via Russian border, but it's faster going via checkpoints.
How to apply for a free pass to cross checkpoints in Lugansk and Donetsk Regions at Security Service of Ukraine website
It's fast and easy to get a pass needed to cross checkpoints in Donetsk and Lugansk Regions. The pass is free, you just need to apply online and it's usually ready withing 10 days. After you get confirmation that the pass is ready you can cross the contact line, all your information with be in the database, so you just need to show your passport at checkpoint. If you don't speak Russian or Ukrainian it may be hard for you to get it as the Security Service website is not available in English language. 1st you need to fill a form at https://urp.ssu.gov.ua/ua/registration/ See the screenshot below. Basically, you just put your first name, last name and you also need to put middle name. You also must put your email address and date of birth. Password should be at list 6 letters. Check all checkboxes and click big green button.
After that you will get email from firstname.lastname@example.org with randomly generated login and password that you entered. And with that login and password you get on the website again and fill all the forms. If you are not Ukrainian resident and don't speak Russian it may be a bad idea for you to go to that area as there are basically no laws and for pro-Russian militants who control Lugansk and Donetsk America is the enemy number one.
Checkpoints in Lugansk Region. Open hours
There is only 1 checkpoint in Lugansk Region. It's located in Stanytsia Luhanska town. Checkpoints are open from 6am till 8pm in Summer time. Starting from September 1 checkpoints work from 7am till 6:30pm. The checkpoint is located just before the bridge across Siverskiy Donets River. The bridge was damaged during military activities, so it's not possbile to cross it by car or bus, it's open only for pedestrians. In the photo below you can see its current condition. The photo was taken by OSCE monitoring mission. About 4 000 people cross this checkpoint daily and it may take 2-3 hours waiting in the line.
Checkpoints in Donetsk Region
There are 4 checkpoints in Donetsk Region. 3 of those checkpoints are relativly close to Donetsk city. All 4 checkpoints can serve both pedestrians and vehicles. So you can go to Donetsk by bus or by car directly. Up to 6 000 people can cross those checkpoints per day. Checkpoints in Donetsk Region operate in same way as in Lugansk Region. Here are the names of checkpoints: "Mayorske", "Mariinka", "Novotroitske" and "Hnutove". This is "Mayorske" checkpoint in the photo below.
How many people cross contact line via checkpoints daily?
Every day more than 20 000 people cross the contact line via 5 checkpoints that operate in Luhansk and Donetsk Regions. The statistics is published by State Border Service of Ukraine at their website http://dpsu.gov.ua For example, on this amount of people and vehicles went via each checkpoint: "Mayorske" - 4950 people and 785 vehicles, "Mariinka" - 5435 people and 1135 vehicles, "Novotroitske" - 4510 people and 970 vehicles, "Hnutove" - 2555 people and 635 vehicles.
Going to Lugansk and Donetsk via Russian border
Some local people go from Lugansk and Donetsk to Kharkiv and other cities in Ukraine via Russian border. In this case no pass is needed, because that part of the border is controlled by pro-Russian militants and there are no Ukrainian checkpoints. Ukrainian citizens can use their local passport to travel to Russia. In case you are not a citizen of Ukraine and want to go to Lugansk or Donetsk via Russia you may need multiple-entrance visa for Russian Federation. You can fly to Rostov on Don in Russia and from there you can take a bus or a taxi to get to Lugansk or Donetsk. But in this case you will be violating border control rules of Ukraine and may get banned from entering Ukraine in future.