I have no specific experience of that type of razor and very little experience of straights (three shaves with mixed results) but I've shaved with a DE for a long time and, while a lot of it is down to preference and there's no 'right' way, I'd say there are two things you could do different:

1 - prep - I'd recommend having a shower and then applying a hot towel for a few minutes before you apply the lather. Is the lather warm when you apply it? Do you kind of massage your face in a circular motion with the brush when applying lather? Also, you might want to consider a preshave - I use Trumper's Limes skin food - to help lubricate the hairs.

2 - direction of shave - I can't speak for everybody but I would say that most people, and general wisdom dictates, that you start out by shaving with the grain (you'll see WTG used here which means With The Grain), that is in the direction that the hairs are growing, bearing in mind that the hairs grow in different directions on different parts of the face so it's a good idea to have a close look at that. After shaving WTG, lather up again (no massage, just apply lather, again warm) and shave Across The Grain (ATG). That's all I need to do to get a fine shave. Some people then go on to lather again and shave, as I think you're doing, Against The Grain (ATG) but most people advise that you do this after your face has got used to shaving WTG and XTG for a few weeks. I don't do it because it irritates my skin and I don't need to.

If you look around here and some other shaving sites you'll find loads of advice and videos to help you get a decent shave but I hope this is enough to get you started.

Good luck!

EDIT: the others were faster typing so sorry if it appears that I'm just repeating their good advice!