voting processes of each one:
SAG: http://www.sagawards.org/faq
Process:
Voting for the Screen Actors Guild Awards® is done in two stages. In the first stage, members of the Motion Picture and Television Nominating Committees review For Your Consideration materials and vote on the nominees.
In the second stage of voting, all active members who paid their November 2015 dues by December 1st will receive voting information and For Your Consideration materials to review and vote for the recipients.
Selection of the Nominating Committee:
The SAG Awards® Theatrical Motion Picture and Television Nominating Committees are newly drawn each April, each made up of 2200 members. The committees are selected by a random sample drawing of active paid-up members.
Members selected to serve on the Motion Picture and Television nominating committees are not eligible to serve on their respective committees again for eight years. This allows more members the opportunity to serve on these important committees.
How to join SAG:
http://www.sagaftra.org/content/steps-join
Oscars:
http://www.oscars.org/oscars/voting
Process:
Regular awards are presented for outstanding individual or collective film achievements in a wide variety of categories. Most categories are nominated by the members of the corresponding branch–actors nominate actors, film editors nominate film editors, etc. However, certain categories such as Foreign Language Film and Animated Feature Film have special voting rules which can be viewed at our Rules & Eligibility page.
All voting members are eligible to select the Best Picture nominees.
Nominations voting is conducted using both paper and online ballots, with online voting being the preferred choice for the overwhelming majority of Academy members. Voting for nominations begins in late December, and all votes are tabulated by PricewaterhouseCoopers.
...
Finals voting is also conducted via online and paper ballots.
During finals, all Oscar categories are on the ballot for voting members.
How to become a "member:" apparently not all members are voting members.
http://www.oscars.org/about/become-new-member
That's likely TMI. But this recent article sums some of it up nicely.
http://www.bustle.com/articles/59938-sag-awards-vs-oscars-how-do-the-nominees-compare-in-this-years-biggest-awards-races
For starters, the voting bodies are different. SAG membership consists entirely of actors, while the Academy is made up of 17 branches that represent the breadth of the film industry (actors, but also directors, writers, cinematographers, costume designers, and more). There are approximately 160,000 actors with SAG cards across the country; the Academy is much more exclusive, with just under 6,000 members as of a 2012 study.
SAG nominees are selected by a smaller committee of 2,100 members that are randomly selected anew every year. (A separate random sample of 2,100 members also votes on the SAG television awards.) Once that smaller sample chooses the nominees, the entire membership gets to vote on the winners. Conversely, Oscar nominees are selected only by their own branch: actors pick the acting nominees, directors the directing nominees, etc. Once the nominees are determined, the entire Academy votes on the winners. This year, the Actor's Branch of the Academy includes 1,176 members who will choose the Oscar acting category nominees, versus 2,100 choosing the SAG nominees.
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