How do I become a civilian contractor to the government?

Understand you may be hired for a contract, and if the contract is lost in a year or two, you may have little notice of termination. Little, like here's a box, please hand over your ID/access card, and log out of your computer immediately.

There are enumerator ways to become a contractor. Which specific area or field are you referencing?

I'm not generally in favor of the government contracting side as a career unless you're specialized in something and you work for Raytheon, Boeing, etc. (Defense Contractor) that the MIL side has to renew contracts with as their products are proprietary (e.g. Trident Missiles). Say you work for some base operations contractor who loses the next round of bidding. The winning bidder gets to reset the salaries back to minimum because that's how they priced it. Although the contract states first vacancy offers go to existing employees, stand by for a pay cut. That has you static where you need to be earning ever more money, building a retirement, etc. Going CS (GS, WG, WD, WL) is an option with usually more upward mobility than time limited contracts. You can buy CS retirement credit by giving them 3% of basic pay back. I did that way back in the day by giving them $10K for 10 years. That is paying out $14K/year now. Show me something with better return. The TSP which matches the first 5% every payday should be an easy slam dunk.

Finally you need to open your eyes to a bigger world. You need two annuities and a hefty 401 to do what you want to do when you don't want to or can't work anymore. The "pay your bills and learn to live on 40%" axiom is useless now as we live longer and don't want to stay at home and knit. You can even overshoot which is even more pleasant. Turn 60, quit, and get a pay raise. Not a bad place to be.

Why do want to be a government contractor versus a government employee? My experience the government employee usually has better stability, long term employment and benefits. But that’s not always the case.
I believe you can use your military TIS to add to your potential government retirement (buy in).

USA jobs is a great site. Also depends on what type of job you are looking for you can google them there are a lot out there. When I worked CRC at fort bliss there were probably about 12 different companies I can remember that sent contractors overseas.