Thank the Lord and sing His praise; tell everyone what He has done. Let all who see the Lord rejoice and proudly bear His name. He recalls His promises and leads His people forth in joy with shouts of thanksgiving. Alleluia, alleluia.
These words are sung after communion in Divine Service setting 1 and 2, but I think they have a lot to say about our thanksgiving. Note first of all that singing accompanies thanks. We show our thankfulness to God by singing His praises. We praise and thank the one who gives us all things. We praise God by proclaiming what He has done. Secondly, we tell others about the great things God has done, those things for which we are thankful.
As we have just "seen" the Lord in, with, and under the bread and wine of the Lord's Supper, we rejoice. We can be proud, in a good way, of the name of the Lord that we bear. We bear the name Christian, the name given us in our baptism. We go forth into the world with this name, telling others what Christ has done, and thanking Him for His saving work.
Why are we able to give thanks? Because the Lord recalls His promises. He keeps His promise to forgive our sins. He promises to lead us through this life, through the valley of the shadow death, into eternal life with Him. For all this we thanks and praise Him.