My 2 cents having worked in Fed Gov for 31 plus years (now retired):
1. Get a copy of job description and qualification. Study them.
If the job requires dealing with clients/public, there may be scenario questions on how to deal with sticky situations such as uncooperative attitude, aggressive behaviour, violence etc. Remember, tact is most important.
2. Do not be afraid to ask clarifying questions if you do not totally understand the question asked. No points deducted in this case.
3. Understand the department you are applying for the job, its mission statement, organization structure. You may be able to get it on the web.
4. Depending on the nature and level of the position, there may be a case study exam. The higher the level, the more involved. Years ago, I had a in-basket exercise which required you to clear miscellaneous actions, memos etc in your in basket. But that's for a manager position. I found out that there was no right or wrong answers. Thinking too much or indecision actually is worse than making a less than perfect action.
5. Other than technical questions, questions on Personal Suitability are equally important. Refer to 1.
I hastily assembled the above. There may be more. I'll post them when I have more.