I worked for an employer with a 403b and contributed, but my new employer only does 401k.
Can I put the money from the 403b into the 401k? How?
You can move money from a 403b to a 401k plan, but the question you should ask yourself is whether it is a wise decision. Unless there are specific reasons for wanting to invest in your new employer's 401k (e.g. you can buy your employer's stock at discounted rates within the 401k, and this is a good investment according to your friends, neighbors, and brothers-in-law), you would be much better off moving the 403b money into an IRA, where you have many more choices for investment and usually can manage to find investments with lower investment costs (e.g. mutual fund fees) than in a typical employer's 401k plan. On the other hand, 401k assets are better protected than IRA assets in case you are sued and a court finds you to be liable for damages; the plaintiff cannot come after the 401k assets if you cannot pay.
To answer the question of "how?", you need to talk to the HR people at your current employer to make sure that they are willing to accept a roll-over from another tax-deferred plan (not all plans are agreeable to do this) and get any paperwork from them, especially making sure that you find out where the check is to be sent, and to whom it should be payable. Then, talk to your previous employer's HR people and tell them that you want to roll over your 403b money into the 401k plan of your new employer, fill out the paperwork, make sure they know to whom to cut the check to, and where it is to be sent etc. In my personal experience, I was sent the check payable to the custodian of my new (IRA) account, and I had to send it on to the custodian; my 403b people refused to send the check directly to the new custodian.
The following January, you will receive a 1099-R form from your 403b plan showing the amount transferred to the new custodian, with hopefully the correct code letter indicating that the money was rolled over into another tax-deferred account.