I play female characters in campaigns about 25% of the time (and about 100% of the time as a GM), so this is something I've worked on/thought about over my gaming career.
Depicting Your Character
First, there's the general "How do I depict anything different from myself at the gaming table?" This is often a problem not just with crossgender play. I remember an activity I did for one long term campaign, I had the players draw the other characters as they saw them. One player, Laura, drew Dave's character as a scrawny little guy. In reality he was a huge buff bodybuilder type. His "big fighter" character had converted and become a cleric before Laura joined the group, and so all she knew was how he presented himself now, which seemed bookish to her. He had established his look with the original players but was failing to carry it through in-game such that a new player (not that new, she had been in the game like a year by this point) didn't have an accurate mental picture of him. He was miffed, but I reminded him that people only know what they see, and in an RPG they only "see" what comes out of your mouth.
So the advice I gave to him is equally applicable to crossgender play. Use opportunities to lift weights/flirt with boys/show off whatever is distinct about your character. Describe yourself from time to time both in the first person - "I flex my pecs to show off" or "I toss my long hair and sniff at him” - and in the third person, “Tristan goes over and picks up the sack like it’s a feather and slings it over his brawny shoulder”. Make sure and reflect your physical form, gender, dress, and demeanor to the rest of the group enough that they keep it in mind. Props can help, sometimes players choose character portraits and make standees or whatnot so people can "see" them (I've used this specifically with crossgender play). Similarly, as a GM I often make character portraits to clip to my screen of NPCs, it reinforces their presence as well as physical details about them including gender. I think 9/10 of the issues with crossgender play in practice aren't "I'm failing to precisely emulate the female mind," but are "Frank looks over at me, sees a guy, and just up and forgets the character I'm depicting is a woman."
The GM can help players with this by "reflecting" the world/NPCs' views of the PCs back to them, which helps cross-emphasize identity across the group. This helps with a lot more than gender; I've lost count the number of times a PC who looks like a glowing gnome with ioun stones whizzing around his head and massive gaping wounds riding a magical beast just wanders up to some peasant and starts chatting them up. It takes them a minute to realize why the peasant shrieks "DEAR CUTHBERT NO" and flees, but then they realize it's because they're so badass looking and they tend to like it. There's right and wrong ways to do this, you don't want to have every night in an inn be "and here's the list of dudes that hit on Georgina." Talk to your GM and say "Hey, using narration and NPCs to reinforce my gender (or whatever!) with the other players would help." In Dave's case above I made a note to refer to his huge frame and muscles more often to reinforce it especially since his chosen role was less martial, and that worked out well.
Now on to the deeper stuff. It can be hard to RP someone different, especially a woman, because a lot of folks are quick to criticize. Some people think crossgender play is "wrong" or "weird" in the first place somehow - I take a dim view of the hangups such people must have, but you have to take it into account. But when you do, you can get a lot of criticism that you're playing wrong or making the character a stereotype.
Now, depicting a stereotype isn't always bad, depending on your game style - heck, if you're playing Feng Shui, for example, all the characters are MEANT to be stereotypes you see in action movies. And if everyone's basically playing characters no deeper than the usual SyFy special starring Eric Roberts, then IMO you're fine to go "hooker with a heart of gold" or "killer vixen" or whatever stock personality the latest Hollywood blockbuster contains. In these cases, you are making female characters (usually) "more different" because stock characters are all about overemphasizing whatever their distinctive points are (think a lineup of anime characters, the "big guy" is always unrealistically like 2x everyone else's size, etc.) "I'm the dark and brooding loner!" Stereotypes are often in scope in gaming.
Draw On Real Women
But let's say you're playing a more "realistic" (for a variant definition of realistic that includes dragon turtles, of course) game and you want to play a person, not a stock character. There, you don't want to "different them up" as much. My primary technique is "observe the women in your life, and respond as they would." (I've lost count of the number of times I've done this and been accused, by a man, of course, of acting out a stereotype, even though I am drawing from an exact real-life situation where the woman I knew did X... But I digress.)
In this way you get away from playing women all the same, based on whatever your preconceptions of "what IS a woman" in some strange abstract sense. I tend to say "Hmm, I want this cybered up space spy to be about 70% my friend Laura, maybe 10% my ex-wife, and 20% Angelina Jolie from that one movie." Just like with any character, sometimes you have an internalized understanding of their motivations, and sometimes you just have them do things that seem like it's what someone would do, even if you don't "get it."
In the end trying to play women, or any kind of character, in an "agenda-driven" way isn't good. Every real person in the real world shares some aspects of stereotypes and differences that are "cross type" and then just have miscellaneous things about them that don't fit or contradict any "type." Trying to play female characters exactly like they're male is unsatisfying and a missed opportunity. If the real world was full of one homogeneous gender, it would probably be quite different. Gender and the tensions surrounding it are what generate a lot of the drama in epics, novels, movies, and every other form of art slash entertainment in the world and RPGs are no different.
Real Play Examples
Our current Pathfinder PC group has a female NPC along who is kinda-but-it's-not-real-defined the girlfriend of a PC. She's half-elf, he's a human. So they were in a town where there were a lot of cross-race couples and she used the opportunity for a "DTR" talk. I as the GM had to depict her well as a woman so that the relationship could develop in a realistic and satisfying way. "So, what do you think about mixed-race relationships?" "Gulp!" Or when they found out she'd been carrying a pair of designer shoes in her adventuring pack "just in case." Little bits like this, they don't have to be pervasive, but all the PCs think of her as both female and realistically complex and realized - even with her name being "Sam" and me not doing funny voices, I don't get any "tell him to magic missile the wraith..."
One of my favorite characters I played was a female, a cleric in the Curse of the Crimson Throne adventure series from Paizo. Sometimes she worried about boys, sometimes she took care of business. Sometimes she was kind and empathetic, and sometimes she was hard. She wasn't a stock stereotype, but none of the other players ever got confused that I was playing a man either, except once or twice, which to me is the sweet spot between acting too different and acting too not different. She ended up becoming Queen once we deposed the current crazy killy one, so I like to think she had a lot going for her.
My previous female character had been a hard-bitten cybered up con woman in a Silhouette game - they really didn't have much in common at all. I was drawing on different personality sources of course.
Also, gender isn't the single biggest issue, being a cyborg or alien or elf or lost race or wildebeest is also a large component of your personality, don't make it all about gender. But the question's about gender so I'm focusing on that.