Direct onsite because I interviewed in the past and did well that time.

From the time I sent my resume to interview day: 2 weeks. From interview day to offer over the phone: 2 weeks.

The syllabus for the interviews is very clear and simple:

1. Dynamic Programming
2. Super recursion (permutation, combination, ... 2^n, m^n, n! ... etc. type of program. (NP hard, NP programs))
3. Probability-related programs
4. Graphs: BFS/DFS are usually enough
5. All basic data structures from Arrays/Lists to circular queues, BSTs, Hash tables, B-Trees, and Red-Black trees, and all basic algorithms like sorting, binary search, median...
6. Problem-solving ability at a level similar to TopCoder Division 1, 250 points. If you can consistently solve these, then you are almost sure to get in with a 2-week brush-up.
7. Review all old interview questions in Glassdoor to get a feel. If you can solve 95% of them at home (including coding them up quickly and testing them out in a debugger + editor setup), you are in good shape.
8. Practice coding: Write often and write a lot. If you can think of a solution, you should be able to code it easily without much thought.
9. Very good to have for design interviews: distributed systems knowledge and practical experience.
10. Good understanding of basic discrete math, computer architecture, and basic math.
11. Coursera courses and assignments give a lot of what you need to know.
12. Note that all the above, except the first two, are useful in "real-life" programming too!