At the beginning of iCarly, Sam and Freddie were mostly hostile towards each other, with Sam's treatment of Freddie even including physical aggression. It seems as though Sam and Freddie tolerate each other only because they are good friends of Carly. And after the creation of their web show, they now have to.
A closer look, however, reveals that most of Sam's insults are mostly about Freddie's body shape (for example, his butt) or his crush on Carly. This suggests that Sam might actually be interested in Freddie and is hiding it due to being afraid of being shot down, which leads to Freddie's insults, which center on Sam being such a huge tomboy. Freddie's insults are less frequent, but they seem to be more hurtful. Sam knows she is not very girly and in Season 2 even attempts to change that. Eventually, the insults and bickering seems to become more of a ritual than a manifestation of actual hate for each other.
In "iWill Date Freddie", Sam pokes Freddie in the stomach, which is teasing but still somewhat affectionate. She also offers a thousand dollars for a picture of Freddie's butt, not that she actually has the money. She takes interest in his first date, setting up his cameras so she can spy on him. Also, Freddie insists that Sam is his friend despite all the mean things she does to him, the first time either of them calls the other their friend. When she finds out that Valerie is just using Freddie, Sam takes the initiative to tell him. Sam and Freddie even hug at the end of this episode, even though that ends in a wedgie for Freddie.
"iWill Date Freddie" is just the start of many milestones in Sam and Freddie's relationship. In "iRue the Day", Sam gives Freddie a compliment for the first time. In "iHeart Art", Sam takes offense when Freddie says she has no self-control, and bets she can go a full week without insulting Freddie. (She fails.) Interestingly, Freddie's attempts to get Sam to insult him include hitting on her:
FREDDIE: You wanna kiss me?
SAM: Kiss you? Dude, I'd rather—not do that at this time but I appreciate your kind offer.
Well, they say third time's the charm. This is only the first.
Sam freaking out over not being able to insult Freddie suggests that her aggression towards Freddie is not part of her overall personality and for some reason she feels a need to pick on Freddie in particular. Since Sam rarely actually hits Freddie and her verbal attacks lack bite (Freddie gladly lets Sam insult him at the end of "iHeart Art" to collect her 40 dollars), it is unlikely that her aggression stems from actual hostility towards Freddie. Rather, it is more likely that her aggression is instrumental, in that she picks on Freddie as a means for something else. However, whatever her reasons are, she keeps them to herself.
In "iHate Sam's Boyfriend", Freddie finally says something nice about Sam, even if it actually makes him physically sick to say it. While not identifiable as jealousy, he does disapprove of the intensity of Sam and Jonah's relationship, even before it starts to affect iCarly. This is in spite of the fact that for once Sam is busy with someone else rather than harassing him.
In "iHatch Chicks", we get to see a more sensitive side to Sam (which is hopefully more appealing to Freddie), who is visibly upset when the last chick got away. However, she stops yelling at Freddie when Carly tells her to. In "iDon't Wanna Fight", Freddie even goes so far to suggest Sam is actually hiding a crush on him, although Sam turns it around and takes a dig at Freddie's manliness. We also get to see Sam's sensitive side again when she cries for the only time that season, in fact because she is moved by Freddie's efforts to patch up her friendship with Carly. In "iGot Detention", Freddie seems to be trying to impress Sam just as much as he is trying to save iCarly. Could he be starting to like her? Sam compliments Freddie on one of his attempts, although it gets foiled.
Sam and Freddie are very competitive, especially with each other, and this comes to a head in "iStakeout". Interestingly, Sam wants a tattoo of herself on Freddie's arm. Also in this episode, Sam's own technical prowess is revealed (she knows what MPEG stands for and Freddie doesn't), and it appears that Sam just may feel a little bit of guilt about harassing Freddie, as she smiles sheepishly when he calls her out for it. Sam also knows Freddie's real name, Fredward, while Carly doesn't. In the end, the tattoo is revealed to be a mere prank.
In a Sam/Freddie doubleheader, in the very next episode, "iMight Switch Schools", the bickering duo work together for the first time without Carly, even if she does resort to abusing Freddie's crush on Carly to get him to do what she wants. Amazingly, they hardly bicker at all in this episode, even in the part before they work together to keep Carly at their school.
Sam and Freddie bet again in "iFence", with Sam winning again. Also, Sam is excited to go to Glitter Gloss and Build-a-bra, a sign that she has shed some of the tomboyishness that made her so unappealing to most boys in the past. When Freddie fences in a match against Doug Toter, Sam is there cheering for him, yelling at the top of her lungs. And she says she hates him...
In "iCarly Saves TV", Sam sticks his finger up Freddie's nose while they are all in the limo. Enough said.
There isn't much Sam/Freddie interaction in "iHave a Lovesick Teacher" or "iWin a Date", other than the usual bickering. Things kick up a gear, however, at the start of Season 2.
When Carly and Sam both fall for Shane in "iSaw Him First", Freddie does everything he can to help Sam out so that Sam ends up with Shane instead of Carly. While, if successful, their plan would hinder Sam and Freddie getting together, it does show the two of them working together once again. There is one notable scene in the episode where Freddie comes across Sam in a kissing booth, one of her plans to get Shane to kiss her:
(Freddie puckers his lips.)
SAM: Not for nine billion dollars.
A markup of 900 billion percent? Pretty steep. But like I said, third time's the charm. In the end, no one gets Shane, Shane gets hospitalized from falling down the elevator shaft, and life goes on as normal for the kids.
In "iStage an Intervention", Sam pranks Freddie, causing him to believe he is experiencing bad luck due to not forwarding a chain email. Freddie eventually catches on, but instead of being mad at Sam, simply joins in at the game. He lets her believe she got him a third time, then fakes a text message appearing to come from the hottest senior in school asking her out to the mall. (Technical note: it used to be possible to fake the source of a SMS text message, but technology may have changed since then.) It is never shown whether Sam catches on or what happens when she gets "stood up". However, the pranks do stop. Also in this episode, we see that Freddie is much more socially adept than the geeks Sam keeps associating Freddie with. But then, if Sam truly considers Freddie a geek, her "kiss a girl" comment is directed at him too. And out of the other girls in the room, it's not like Carly or Sasha Striker would kiss him.
In "iOwe You", Freddie calls Sam out for defaulting on all her debts. Surprisingly, Sam cares very much about how Freddie thinks of her and even goes as far as getting a job so she can finally pay him (and Carly) back. Even though she hates the job, she sticks to it until Carly hatches a plan to bail her out, thanks to Spencer's legal advice which allows Sam to keep the money iCarly fans have been sending her. We also get to see that Freddie knows Sam better than even Carly when he says Sam would not simply accept the money if Carly just gave it to her. Finally, there is also a cute scene were Freddie tells Sam she's wanted by the school principal.
In "iHurt Lewbert", Mrs. Benson taking care of Lewbert allows Freddie to be a free man for a few days, and boy does he jump at the opportunity. Freddie even tells Sam that he slept naked save a pair of socks, with the clear intention of making Sam uncomfortable. It appears Sam does imagine Freddie naked, and the thought of it causes it to lose her appetite, no trivial task considering Sam's constant penchant for food. Despite the horror of imaging him naked, Sam pulls down Freddie's pants anyway. Also Freddie is freaking out over becoming Lewbert's stepson, Sam for once drops her insult when he tells her to.
In "iGo to Japan", Sam and Freddie hug, and Freddie pokes Sam's stomach, as in "iWill Date Freddie". Only this time, the hug is not followed by a wedgie, and the poke is not coupled with an insult.
After this, the Sam/Freddie growth does slow down a bit, unfortunately. In "iPie", there is little positive Sam/Freddie interaction. However, when looking for the pie recipe, Sam fights for control of the computer, apparently willing to be geeky in front of Freddie, even though she's always picking on Freddie for being one. For once, their constant fighting has a positive outcome in that they knock over the computer and find the recipes hidden inside the case (rather than on the file system).
" iChristmas" has a little bickering in the beginning, but since this is Carly's fantasy episode, they don't interact again until the end. It is interesting though that in Carly's vision, Freddie falls for the obnoxious mean girl. Only Rona is much worse than Sam in her treatment of Freddie. More notably, Freddie hasn't hit on Carly for two whole episodes, breaking a trend of putting in a tiny Carly/Freddie moment in each Season 2 episode before that.
This leads us to the upcoming "iKiss". Like I said, third time's the charm.