There is a wealth of information on rat introducing techniques on the web, including here.

So, rather than re-inventing the wheel when such good information is already out there, I will over-simplify the process for a short read. Considering it can mean a rat's life if introductions do not go well, it is obviously highly recommended that you read more on the subject (see 'Introducing Rats to Rats').

I will include this quote, because it is quite important:
"Rats are very territorial and instinctually defend their territory against intruding strangers, trying to drive them away or even kill them. Introducing a new rat(s) into your rats' existing territory would be disastrous."

Sometimes you will not need every one of these steps but often you will. If things aren't going well in one step, go back a step for a while longer. Familiarize yourself with what normal play looks like. There is a saying that often applies, "No blood, no foul" meaning if they are wrestling and no blood is involved they are likely playing or working out dominance.
  1. Position cages next to each other but not so close that rat fingers or tails can be bitten off. Leave them this way for at least a couple of days. You may also begin to swap some cage items between cages to introduce smell. Try a cloth in each cage then swap them the next day.
  2. Swap cages. Existing rat goes in new rat's cage and new rat goes into existing rat's cage. Swap back the next night. Swap again the next. Help them build familiarity without actual interaction.
  3. When you are ready to begin introductions, clip nails, especially on the back feet. Dab a bit of vanilla extract on the rats' noses and genital areas. Get yourself some heavy gloves and have them on during intros to break up a fight or to use as a barrier between them while they interact. Have a towel nearby for separating angry rats.
  4. Choose a neutral introduction area such as a bathtub, table, or bed. Sometimes it can help to sprinkle some Rice Krispies down. Insert rats and watch for signs of aggression such as puffy fur, arched back and hissing. Intervene, separating them with your gloved hand as needed, before it escalates into a full fight. Your goal is to allow them to interact without fights for a while, then separate again while ending on a high note. You may need multiple sessions of this.
  5. Sometimes the, "Scary car ride in a carrier together while bonding" trick works but have a friend along in case fighting erupts. Driving and stopping fights doesn't mix.
  6. Some people move recently introduced rats into a neutral cage for a few days to allow them to bond without territorial issues. You might also try them bonding in the new rat's cage but be aware the new rat could have his own territory in that cage.
  7. Clean existing rat's cage well and rearrange some of the things in it. Insert new rat first then existing rat. Watch for aggression signs. There will likely be some dominance "discussions" over the next couple of days but if blood isn't involved it's something they will need to work out.
To reiterate, take your time reading about this and don't rush your introductions!
Here is a recent post with some additional ideas.