Because most of tatting is worked in the round, finishing a piece starts with the beginning. If you want to avoid a lot of tying and cutting of threads for a piece with multiple rounds, such as a doily, think about how you are going to start even before you wind your shuttle. A lot of patterns simply tell you to fill the shuttle with a certain amount of thread, make your first ring, then join the ball thread to start the first chain. If you are using the same color thread for your rings and chains, don’t cut the thread once you have filled the shuttle. Simply start your first ring on the thread between the shuttle and the ball, then when you are ready to start the first chain, the ball thread is already attached and you won’t have any loose threads. When you get to the end of that round, you can make a join into that space at the base of the first ring made and tie the ball and shuttle threads together there, or use another method of weaving in the ends.
If your pattern starts with a chain, you can still do the same thing, but you will need a “stopper” so the chain stitches don’t unravel themselves. One suggestion for this “stopper” is to fold the thread over the opening side of a safety pin, hold the safety pin between your working fingers and make the first stitch as usual, pulling that knot up as close to the safety pin as you can. Once you are done with the round, remove the safety pin and you have a tiny “picot” that you can use to join into then tie and cut the threads or weave in the ends, whichever finishing method you prefer.
If you are tatting with two shuttles, it’s a little more tricky, especially if you don’t know exactly how much thread you will need or how much your shuttle holds. If you don’t know how much thread your shuttle holds, wind one shuttle full of thread, mark the end with a piece of tape or something that won’t discolor or damage the thread and won’t come off with handling, then unwind the shuttle and measure how much thread you had on it. Then you can rewind that shuttle until it is full again, then pull that much more thread off the ball, cut it, then fill your second shuttle starting from that cut end. Now you have two shuttles full of thread joined together and you can start your design anywhere in between them.