When introducing new dogs, bear in mind that first impressions count for SO much.
You need to do everything you can to set both (or all) dogs up to have the best possible first meeting, and to create the best possible first impressions of one another.
This means meeting in a calm, quiet place that is neutral territory for both dogs. If you are introducing a new dog to several resident dogs, do this one dog at a time. Make sure the dogs plenty of space to get used to one another’s presence.
Off lead is really too much of a risk, so long lines and harnesses are the best way forward. Walk the dogs around a big space, ideally a secure field, with them a long way apart from one another. Ideally, play follow-the-leader, so that each dog can pick up scent from the ground that the other dog has walked over. Walk in a big circle or loop. They need to be far enough apart so that neither dog feels the need to react, and both dogs can take high-value rewards from their respective handlers.
Gradually reduce the circle. Each dog should be allowed to sniff and look, but encouraged with rewards to keep moving. Gradually catch up and walk parallel, again with enough space between the dogs so that no dog is reacting, and each dog can focus on their handler.
Throughout this process, keep leads nice and loose, be interesting and rewarding, and avoid any telling off or ‘correction’. We want the dogs to associate one another with low stress, high reward, and calm activity.
If at any stage a dog does react, just increase the space and get your dog’s focus back on you using rewards.
When you can walk the dogs close enough to each other that they could sniff each other, but with no reaction, have one of you drop back a little so they can sniff butt. Keep this first greeting really short and positive. Maybe three or four seconds. Then, in a happy voice, say ‘let’s go’ and return to parallel walking. Repeat a minute or so later.
This allows the dogs to get used to one another, without there being time for anything to go wrong.

If you are in a secure space, now you can consider allowing them to choose what they do. So, drop the leads and let them drag behind them. Allow them to interact, but be sure to recall them frequently before any play can get giddy or over the top.
Reward well, and send them back to play again. If you do this and either dog ignores the recall, use the long lines to split them up. Get their focus back on you before allowing them back together. It’s important that when this happens, BOTH dogs are brought back under control. If you have one dog loose trying to play, and the other dog secured on a lead, that’s a recipe for something to kick off.
Once all the above is done, then, if it’s just the one dog you are introducing to another, walk them both home and enter the house together.
Ideally, I would put away all toys and highly-prized items such as bones, chews etc. Provide multiple beds and water bowls. So, three or four beds, three or four water bowls. This is so that the value of these items are reduced, along with the chance for competition between the dogs.
Feed them in separate rooms to begin with. Introduce toys and treats gradually as the new dog settles in, supervised by one adult per dog.
The above is the ideal practice. This isn’t always possible, so if necessary, remember to keep things calm, give dogs space, avoid tight leads, head-on meetings, and potential competition over food/toys.
If the dogs get on well, then remember it is important for both dogs to have lots of one-to-one time with their people, as well as spending time together.