How do I get an entry level job doing UX if I have no direct professional experience? I am asking is there something I can do on my own to build up a UX portfolio?
Well, my temporary solution is to try to post answers on UX.SE :)
Seriously though, a UX portfolio can be blocked by a lot of issues:
Reasoning is long and tedious, and it doesn't look cool. It's so easy to hide the truth on a third of an A4 / US Letter page.
Also, imagine a portfolio of a civil engineer who does water pipe systems. If he is the best in his job, it means you never realized he even had one: it just worked. Portfolio-oriented thinking just brings you to the shooowy side.
I think the need for a portfolio is about reputation. You can gain reputation within a community. When the webpage is done by the 16 year old son of the CEO of a company, that son has built up reputation inside the management about being a good designer - albeit not necessarily in the right place, the right way.
In order to gain a much more serious reputation you have to be part of a community, where people who actually need UXers are present, and you have to show you're a worthy one.
This could mean going to meetups in your local town, going to UX conferences, hanging around on forums, or just simply showing off UX demos at your current workplace on how you could improve the situation. You need to show off how cool you are not to the world, but to a small part of it where you could expect to get a job.
And there, honestly, you don't need to be the best world-wise. Still, I'd like to recommend: "measure yourself to the Infinity" : it's really hard to fix the errors and argue with those local maximum guys, who don't even realize that there's a Mount Everest out there in the Himalayas.
First of all, ask yourself why you want to work in a field such as UX. You say you don't have direct professional experience, does that mean you have been working on a similar field? If the answer is yes, if you have experience in web / interface design, then you are already doing UX design, even if it's not your 'professional definition'.
As mentioned in the comment, the best way to show you know your way around UX is to demonstrate so in your portfolio.
In my case, I started as a web designer and later decided I wanted to focus on interfaces, because that was what attracted me the most. Lots of things have already been done in web, and we are so used to navigating through thousands of different and good sites that it's not that difficult to create a 'correct' UX, sometimes it even comes from mere common sense or intuition. Interfaces can be a bit trickier because of specific functionalities (and usually space limitations), so what happened to me was that I realised I needed to do a deeper research and explain (to myself and my clients) why things were done in a certain way. After a while, I realised I was truly fascinated by the theory behind the design. And now I tend to say I do interaction design... even when it sometimes means I do the exact same thing I was doing before, it has the extra spice of analysing every decision I make from the user's point of view. I got my current job using my portfolio, and explaining why I had gone in a certain direction with a design instead of another one.
So in short, if you have been designing you have already done half (or more) of the job. Conscious decisions, scenarios evaluations... Truth is, in my opinion, there shouldn't be a difference between a web portfolio and a UX one.
I started in a cross-functional UX team (probably not truly UX at the time) as the lead front-end developer. From there, I took part in brainstorming sessions and took an active interest in the other disciplines my co-workers were dealing with and eventually I was spending a third of my time doing interaction design and product development.
If you can't find an entry-level UX gig, find a cross-functional team that requires your current skillset and learn from your co-workers and show your interest and eventually you'll have a professional portfolio of UX work on top of your current portfolio.
Well, I was in the exact position as you are right now and this is what I did.