Easy way of doing it is the same as the easy way of having any other LGBT character in a game. Don't bother to bring it up except as part of what makes that character 'them', in terms of characterisation. Naturally anything like being gay or being trans would have some effect, however small, on the personality of that character, just as being black or Asian would, or being intelligent or being stupid would, or whatever. It's all part of that character's personality, and how they developed. If you want to write a well-rounded, well written character, then you have to consider everything about them, and what makes them the person they are, and that's the only thing you should be thinking of. Otherwise, if it's not plot related, don't bother bringing it up anyway, even if 'Word of God' from you as a writer or whatever is that a specific character is whatever they are.
Case in point, I'm starting to write the concept and story for a game I have planned, and the main character is bisexual. This doesn't ever get brought up except with a few hints dropped that are part of her journal, which is a major part of the gameplay. I only mention it anyway in the game because it's part of the plot and part of her development as a character, since part of the plot is driven specifically by a love triangle she finds herself in with her ex-boyfriend and a female friend who is openly lesbian - the plot itself is driven by a conflict between them, and focuses on plenty of topics, not just any of the characters being LGBT. If the plot didn't call for this then I wouldn't ever mention in-game that any character is LGBT, because it wouldn't make any difference whatsoever.
The most important thing to remember when writing any character, whether they have a specifically defined race, gender, religion, sexuality, or anything else, is that at the end of the day they are all people, and will be normal people regardless of these other traits. Hence it's ultimately unimportant in the grander scheme of things. (Look at Neil Gaiman's 'Neverwhere', for instance - he's confirmed outside the book that two characters are gay yet we never find out who, and only have very subtle hints to one of them in the text... I have my suspicions on the other but it's ultimately irrelevant
).