As almost all of us have noticed at one time or another, there is server/connection issues hindering your Pokemon Go experience. It's mostly just a matter of servers being overloaded with far more players then could ever have been anticipated. Hopefully upgrading these servers is being treated with the highest level of extreme urgency possible, considering the billions this is generating...
But for now, what do we do?
1. The best way for the time being is to check the charts and maps here http://downdetector.com/status/pokemon-go to determine if you even stand a chance. If your area is red, and the chart/graph indicated there is a recent surge in outages, then it's probably best to wait a while. There will always be some online traffic, especially in certain areas, but by analyzing the fairly straight forward info on this site, it is pretty easy to determine if it is a good or bad time to go out.
Other techniques include:
2. Well servers are most prone to being overloaded during peak times. After school, lunch break, Weekends. If you can plan to play on an off time it'll help. You must keep in mind time zones, and how an off time for you may be a peak time for a nearby area. It is tricky, and population-Pokemon go user ration dependent, but it is possible to figure out. Ex. North America is general more densely populated around the coasts. So yes there are many time zones, but the central area of the continent wont put as much of a burden on the servers as the coasts. So yes factor it in, but not accordingly.
3. Better hardware, and being on a faster network can contribute to being one of the people to squeeze through the bottle neck of players all trying to log on at the same time, but ultimately if the server is down it's down and better hardware wont necessarily make the difference.
4. If you want to dedicate more system resources towards it without buying a new device, try closing background process and anything that is unnecessarily open prior to launching the game.
5. Also restarting the phone once in a while clears out the ram, and gives it a clean slate to run on, which will help.
6. If you've caught a pokemon, or just leveled up and it freezes. Try waiting a minute. 95% of the time it'll remain frozen, but aside from the small chance it might actually load after all, waiting a little gives a chance for some of the vital information to pass through behind the scenes, even if the screen is frozen. In other words, if I catch a Pokemon and log off the second I suspect it's frozen, I sometimes lose it. If I wait a minute before relaunching the app, then I almost always have it in my list and have therefore caught it.
7. Trying time and time again is worth is for a little bit, but don't spend forever on it. If it's not working it's not working. Sitting there until it works will make time feel like it's passing more slowly. If anything it'll put more pressure on the server, so it's better to just back off if a few tries don't cut it. Just carry on with your walk and try again in 5-10 minutes. Try to get your mind off of it for a minute, catch up on something else, whatever you need to do. Just don't use an incense in game if you're starting to notice server issues...
Good luck, hopefully this will be under control soon.